In the afternoon, the former president visited a manufacturing facility near Grand Rapids before holding a town hall event in the Detroit suburbs that started around 90 minutes late and ended after just a half-hour.

At the second event, in Warren, Mich., Mr. Trump vowed, if Congress did not act, to use executive action to enact protective tariffs to limit the flow of imports from China and other countries that he said were killing jobs in the state.

“The word ‘tariff’ I love,” he said at Macomb Community College, where he was joined onstage by Senator Marsha Blackburn of Tennessee, one of his staunchest allies in the Senate who served as the town hall’s moderator.

Mr. Trump fielded a handful of friendly questions from his supporters that set up familiar talking points and lines of attack. He said Americans were forgoing certain comforts because they could no longer afford them under the Biden-Harris administration.

“We don’t order bacon anymore,” he said. “It’s too expensive.”

Macomb County, a working-class area north of Detroit, backed Mr. Trump in both 2016 and 2020. His visit to Michigan came one day after voters in the state began receiving absentee ballots.

Ms. Harris met with Border Patrol agents on Friday in Douglas, Ariz., her first visit to the U.S.-Mexico border since she became the Democratic presidential nominee.

Hours earlier at his first Michigan event in Walker, Mr. Trump went on a 25-minute-long diatribe about the Biden administration’s immigration policy. Mr. Trump, who was convicted of 34 felony counts in Manhattan and whose 2020 election lies spurred an attack on the Capitol, called Ms. Harris’s border policy a “crime,” saying “there’s no greater act of disloyalty than to extinguish the sovereignty of your own nation.”

Mr. Trump once again broadly depicted immigrants as “killers” bent on invading the United States, a characterization that border authorities have said ignores that many migrants are families with children. He pointed to Immigration and Customs Enforcement data reported earlier on Friday by Fox News that found 662,566 noncitizens with criminal histories on the agency’s national docket.

But the data does not bear out many of Mr. Trump’s claims about immigration, including his insistence that undocumented immigrants are causing a crime spike in the United States, a contention that available national data does not support.

And at one point, Mr. Trump acknowledged that he has made some of his immigration claims — including his continued insistence that other countries are deliberately sending prisoners and the mentally ill across the southern border — without evidence, then maintained that he had not needed it anyway.

“They’re dumping them in our country, and I never had proof,” Mr. Trump told hundreds of people at a manufacturer in Walker. He added, “You know why? It’s common sense.”

Mr. Trump’s advisers have been eager to get him to focus on policy, particularly around immigration and the economy, two areas where polling has shown dissatisfaction with Democrats.

As he often does in Michigan, he singled out autoworkers and the auto industry, which have long been central to the state’s economy. He criticized Ms. Harris’s tax plans and once again promised to impose a tariff of 100 percent or more on every single car coming across the Mexican border, a proposal that could potentially violate the United States-Mexico-Canada Agreement negotiated by his administration.

And as he was talking about his proposed tax cuts, he stopped briefly to acknowledge people leaving his event before he was finished, falsely insisting that people do not leave his rallies early and that “when they do, I finish up quick.”

At their debate, Ms. Harris rankled Mr. Trump when she suggested people were leaving his events early because they were bored and exhausted. On Friday, Mr. Trump told the crowd that those leaving early were headed backstage to take photos. Some of them likely were doing so, but the crowd behind the press riser had already thinned out well before he made that remark.

In a sign of Michigan’s importance, Ms. Harris issued a statement ahead of Mr. Trump’s visit in which she criticized him for favoring corporations over their workers and for failing to deliver on his promises about manufacturing while he was president.

Arguing that Mr. Trump’s trade deal cleared the way for companies to outsource jobs to Mexico, Ms. Harris said, “We’ve seen this movie before. Once again, he is repeating the same playbook and telling the same old lies about how he’ll fight for working people, including those in Michigan.”

According to New York Times polling averages in the state, Ms. Harris and Mr. Trump remain in a tight race in Michigan. Still, Ms. Harris has held a narrow edge over the last month, and her replacing Mr. Biden on the Democratic ticket significantly cut into a lead that Mr. Trump seemed to hold for months.

At his town-hall event, Mr. Trump sat near a prop: a 1967 Chevrolet Camaro. He was asked by one of his supporters what was one of his favorite American-made cars. His answer: Cadillac. He said that his late father, Fred Trump, would buy a dark blue Cadillac every two years.

“I buy a lot of them for different clubs and things,” Mr. Trump said of Cadillacs, adding, “Great question.”

Ms. Harris’s remarks on Friday in the border town of Douglas, Ariz., laid out a vision that makes clear that her party — and the nation — continue to back away from the long-held American promise of protection to desperate people fleeing poverty and violence abroad no matter how they enter the United States.

“The United States is a sovereign nation, and I believe we have a duty to set rules at our border and to enforce them,” Ms. Harris said. “I take that responsibility very seriously.”

In political terms, her visit to Arizona — a critical battleground state where she narrowly trails Mr. Trump in polls — represented an attempt to toughen her image on immigration, an issue on which surveys show that many voters favor the former president.

On Friday, she spoke at a community college on a stage adorned with signs that read “Border Security and Stability.” Before her speech, she visited U.S. Customs and Border Protection’s port of entry in Douglas, walking along a section of border wall that the Obama administration built in 2012. Border agents also briefed her on efforts to stop fentanyl smuggling.

Ms. Harris had visited the border only once before as vice president, in 2021.

On this trip, she made clear that she would continue to embrace Mr. Biden’s executive order in June to ban asylum for those who cross illegally, regardless of what happens with a bipartisan immigration bill that she has largely focused on in previous speeches. The bill included similar restrictions on asylum, but it has remained stalled in Congress. Mr. Trump persuaded Republicans in the Senate to scuttle the bill this year, a point Ms. Harris often makes on the campaign trail, accusing him of prioritizing politics over good policy.

In Douglas, Ms. Harris hammered Mr. Trump in unusually harsh terms, not just on the border bill but also for what she called his failure to address immigration as president.

“He did not solve the shortage of immigration judges,” she said. “He did not solve the shortage of border agents. He did not create lawful pathways into our nation. He did nothing to address an outdated asylum system.”

And she condemned the policies he did embrace, saying that his family separation policy “ripped toddlers out of their mothers’ arms” and “put children in cages.”

Still, Ms. Harris also used her visit to emphasize a need for a comprehensive immigration overhaul. Throughout the campaign, she has tried to strike a balance between enforcement and upholding the nation’s history of welcoming immigrants.

“We must reform our immigration system to ensure that it works in an orderly way, that it is humane and that it makes our country stronger,” she said in Douglas as she called for legal pathways for citizenship for undocumented immigrants living in the United States, including farmworkers and the group of Americans known as Dreamers, who were brought to the country illegally as children.

Ms. Harris’s trip to the border underscored how much the situation has changed there, as a decrease in crossings made her visit politically possible. The number of border arrests peaked in December, when around 250,000 apprehensions were made. Since June, when Mr. Biden issued his order, the administration has seen some of the lowest arrest figures of the last few years. In July, 56,000 arrests were made. In August, it was more than 58,000, and September appears on track for similar figures.

The overall drop in border crossings has been felt in Arizona. In December, in the Tucson region of the border where Douglas sits, agents made more than 80,000 arrests. This summer, the situation has been much different. In July and August combined, agents made more than 23,000 arrests in the area.

Mr. Biden’s asylum order is able to be lifted if the number of arrests dip below 1,500 for a week. On Friday, Ms. Harris’s campaign said she would go further than Mr. Biden by making the restrictions harder to lift. She would require that “the number of average border crossings be lower for longer before the shutdown can be lifted,” a campaign statement said.

For its part, the Biden administration plans next week to try to cement its restrictions into the asylum system by extending the length of time the numbers must remain under 1,500 to several weeks.

Many voters say they believe Mr. Trump would handle the border better as president than Ms. Harris. But the gap between the candidates has been shrinking in some polls, as the vice president has emphasized border enforcement more than overhauling the nation’s immigration system.

Matt Barreto, a pollster for the Harris campaign, said his surveys had found that Ms. Harris’s approach was matching the mood of voters.

“Voters want to hear about solutions on the border — all voters, white voters, Latino voters, Black voters,” Mr. Barreto said. “Voters want to hear, What are elected officials going to actually do to address the broken immigration system? And there was very high support for the bipartisan border security bill.”

But Ms. Harris’s visit was far from a prime-time spectacle. She chose to make her speech in Douglas on what was Friday evening on the East Coast, guaranteeing it would receive more limited coverage from the news media as a hurricane battered southeastern states.

She has stumbled before on immigration. Early in her tenure, even members of her party criticized how she handled a diplomatic portfolio given to her by Mr. Biden to address the root causes of migration. In 2021, she responded defensively when an interviewer asked her why she had not yet visited the southern border, saying that she had not been to Europe either.

Mr. Trump on Friday dismissed Ms. Harris’s trip as a political stunt, saying during a rally in Michigan that she had gone there only because “she’s getting killed on the border.”

Mr. Trump has called for mass deportations of undocumented immigrants, a hugely expensive and impractical proposal that would most likely require the construction of vast detention camps and the hiring of thousands of law enforcement officers.

Karoline Leavitt, a spokeswoman for the Trump campaign, said Ms. Harris’s “last-minute trip to the border and empty calls for more security 39 days before the election will not rewrite the past 44 months of chaos, crime and bloodshed caused by her open-border policy.”

Immigration is one of the top issues for voters in Arizona, a state Mr. Biden narrowly won in 2020. Repeating that feat seems possible for Ms. Harris, but it will be tough.

Her level of support in Arizona is lower than in the other six top battleground states, according to New York Times polling averages. Recent surveys have found Mr. Trump building on his slim advantage there, at a time when Ms. Harris had not held an event in the state since early August.

Instead, her travel schedule and her campaign’s advertising budget have prioritized the “blue wall” states of Pennsylvania, Michigan and Wisconsin. Ms. Harris’s likeliest path to the White House involves winning those states, not Arizona.

While polls show that many voters want action on the border, some doubt that either party is capable of producing it.

Victor Matamoros, 59, of Phoenix, said he wanted to curb immigration but felt let down by both Democrats and Republicans.

“Trump never built the wall like he promised,” Mr. Matamoros said in an interview this week. “And Harris — I don’t feel very safe with her, because she doesn’t have any experience.”

Reporting was contributed by Jazmine Ulloa in Washington, Kellen Browning in Phoenix and Michael Gold in Walker, Mich.

The senator’s explanation came under scrutiny on Friday after The Washington Post reported that he had said in a private message on social media in February 2020 that Mr. Trump had “thoroughly failed to deliver on his economic populism.”

Ammar Moussa, a spokesman for Vice President Kamala Harris’s campaign, said in a statement that it was “hard to conceive of a more scathing and definitive rejection” of Mr. Trump.

The Trump campaign responded to the messages reported by The Post by noting that Mr. Vance had voted for Mr. Trump for re-election in 2020. The campaign did not dispute the accuracy or the existence of the messages, attributing them to an exchange with a consultant. (The Post did not identify the recipient.)

William Martin, a spokesman for Mr. Vance, said in a statement that “it’s no secret” that Mr. Vance had been a “critic of President Trump in the past.” He said that Mr. Vance’s criticism was not directed at Mr. Trump, but at “establishment Republicans who thwarted much of Trump’s populist economic agenda.”

The campaign also noted that Mr. Vance had said in a 2019 interview with The American Conservative that the Trump presidency had been “more of a success” than he had expected. In the same interview, Mr. Vance blamed Mr. Trump’s lack of success in office on recalcitrant Republicans in Congress.

Also on Friday, footage circulated on social media showing Mr. Vance asserting in a Senate hearing last year that car-seat regulations had driven down the number of babies born, drawing mockery from his critics.

“What I worry here is that in the name of safety improvements — and I don’t doubt that there are marginal safety improvements — we’re actually proposing a change that would make things much, much more miserable for parents for very little marginal improvement in safety,” Mr. Vance said at the hearing, which was about consumer protections in air travel.

“One thing that I really worry about, and I think both Democrats and Republicans should worry about, is we have some real demographic problems in our country,” he said. “American families aren’t having enough children. And I think there’s evidence that some of the things that we’re doing to parents is driving down the number of children that American families are having. In particular, there’s evidence that the car-seat rules that we’ve imposed — which, of course, I want kids to drive in car seats — have driven down the number of babies born in this country by over 100,000.”

The Trump campaign did not immediately provide further comment on Mr. Vance’s car-seat claim.

A recent study did estimate that costs associated with car seats had, in fact, led to at least 145,000 fewer births in the United States over four decades.

John S. Santelli, a professor of population and family health at the Columbia University Mailman School of Public Health, questioned that idea. “As a pediatrician who studies U.S. and global fertility, I see no scientific evidence that regulations around car seats or use of car seats reduces birthrates,” he said in an email. “They do help kids survive motor vehicle accidents.”

America’s falling birthrate has been a core concern for Mr. Vance.

In July 2021, Mr. Vance told Tucker Carlson on Fox News that it was “just a basic fact” that the country was led by a “bunch of childless cat ladies who are miserable at their own lives.” The Harris campaign has used the remark to cast Mr. Vance as out of touch with women, who by a significant margin favor Ms. Harris over Mr. Trump, according to polling.

Mr. Vance will have perhaps his most high-profile moment of the campaign when he joins Gov. Tim Walz of Minnesota, Ms. Harris’s running mate, in a CBS News debate on Tuesday.

Michael C. Bender contributed reporting.

Mr. Trump did not fault the Russian leader for the invasion or for the illegal seizure of territory or for the thousands of Ukrainians he has bombed out of existence. Instead, the former president described the situation as if it were a dispute between two parties operating in good faith that could be resolved in a “fair deal,” but only if he returns to the White House.

“I’ve been saying that I believe if I win, we’re going to have a very fair, and I think, actually rather rapid deal,” Mr. Trump said. The war, he added, “should stop, and the president wants it to stop. I’m sure President Putin wants it to stop. And that’s a good combination. So we want to have a fair deal for everybody.”

Mr. Zelensky is in a difficult position with Mr. Trump. He knows Mr. Trump has a solid chance of winning in November, and that if he does, he will immediately face a decision over how much support to give to Ukraine and what posture the United States will take in the conflict. Earlier this week, Mr. Zelensky made mildly critical comments about Mr. Trump that almost scuttled their meeting.

As he stood alongside Mr. Trump on Fox News on Friday, Mr. Zelensky was diplomatic but struggled to make clear where he thought the blame resided.

“This war shouldn’t be started, and I think that the problem that Putin killed so many people and, of course, we need to do everything to pressure him to stop this war,” Mr. Zelensky said. “He is on our territory, that’s the most important to understand. He is on our territory, and how to stop the war to pressure him as we can. As we can — we have to do it.”

The two leaders had just spent roughly an hour together in the conference room on the 25th floor of Trump Tower on Friday morning. They were both in uniform. Mr. Trump wore shiny dress shoes, a blue suit and a long red tie. Mr. Zelensky was in work boots, cargo pants and an olive-green sweatshirt.

The last time they were together, in September 2019, Mr. Trump was in the middle of a scandal — one of the biggest of his presidency — over a phone call he had made to Mr. Zelensky in which he pressured the Ukrainian leader to investigate his political rival, Joe Biden.

Now, only six weeks before Election Day, Mr. Zelensky had arrived as a wartime leader to shore up a shaky relationship.

Before the meeting, as they emerged from double doors together, Mr. Trump and Mr. Zelensky paused at the head of a large conference table to deliver brief remarks to reporters.

“I think that we can work out something that’s good for both sides,” Mr. Trump said, insisting that if he won the election, he would be able to end the war even before taking office on Jan. 20.

Mr. Zelensky has previously expressed skepticism over Mr. Trump’s claims that he could rapidly end the war. And Mr. Trump’s public statements over the past two years have given the Ukrainians plenty of reasons to be concerned. He initially described the 2022 invasion of Ukraine by Mr. Putin as an act of “genius.” And he has repeatedly insisted that he could resolve the conflict within 24 hours — a message that some in Ukraine take to mean that he would pressure them to capitulate to Russia.

“We have common view that the war in Ukraine has to be stopped,” Mr. Zelensky said on Friday as he stood beside Mr. Trump. He added: “And Putin can’t win, and Ukraine has to prevail.”

Mr. Trump’s assertion that both sides want a deal sidesteps a core question: Whether leaving Russia with a part of Ukraine — it now controls around 20 percent — rewards aggression, and would only lead in time to another Russian invasion, perhaps in Ukraine, perhaps elsewhere. It takes no moral position on whether invading sovereign nations is a fundamental violation of international law.

Despite Mr. Trump’s statement, “there is zero indication that President Putin is interested in a peace deal that would — or should — be acceptable to Ukraine or NATO,” said Seth Jones, a former Defense Department official who is now a scholar at the Center for Strategic and International Studies.

Mr. Jones said that Mr. Putin “wants to hold onto Ukrainian territory that he has conquered by brute force, neuter Ukraine’s ability to defend itself and make Ukraine a Russian client state. This type of ‘deal’ would put countries on NATO’s eastern flank, such as Poland and the Baltic States, in grave danger of future Russian aggression.”

Richard N. Haass, a former national security official and senior diplomat who is the president emeritus of the Council on Foreign Relations, said the Russian leader “has made clear he wants a deal that is one-sided and gives him territory permanently.” He noted that making diplomacy work will require “keeping the pressure on Russia by keeping the U.S. support going, and it’s not clear Donald Trump wants to continue that.”

Morgan Finkelstein, a campaign spokeswoman for Mr. Trump’s Democratic opponent, Vice President Kamala Harris, said in a statement, “The only Ukraine deal Trump wants is one that benefits Putin, not Ukraine.”

Mr. Trump has not directly answered whether he wants Ukraine to win the war, and it’s unclear what any such victory would look like. Mr. Zelensky wants more American weapons, and his plan is to strike back harder at Russia, with continued attacks inside Russia’s borders. While it seems unlikely Ukraine will be able to remove Russia entirely from its territory, Mr. Zelensky wants to put pressure on Mr. Putin to build up a stronger negotiating position for a peace deal with security guarantees for Ukraine.

Mr. Zelensky told reporters at Trump Tower that he was there to discuss his plan to bring about a “just peace.” He was careful to remain apolitical in his remarks. Mr. Zelensky has tried to maintain good relations with both Republicans and Democrats, given that the Ukrainian military relies on bipartisan support from Congress for the continuing supply of high-powered weapons. Mr. Zelensky emphasized that he had met with both presidential candidates this week.

But his efforts on Friday morning to stay out of U.S. domestic politics lasted about three minutes.

Mr. Trump immediately dragged the Ukrainian leader back into an episode that tested the relationship between the two countries when he was president. Mr. Trump said, admiringly, that Mr. Zelensky was “like a piece of steel” for the way he had handled the aftermath of the phone call between the leaders in 2019 that led to Mr. Trump’s first impeachment.

At the time, Mr. Trump was holding up aid to Ukraine to increase his leverage over Mr. Zelensky, whom he was pressing to open a corruption investigation into the Biden family. Mr. Zelensky said publicly that he had felt no pressure on the call — a statement Mr. Trump emphasized as the basis for his warm feelings toward the Ukrainian president.

“He said, ‘President Trump did absolutely nothing wrong,’” Mr. Trump recalled, misquoting Mr. Zelensky, who stood beside him awkwardly. “He said it loud and clear, and the impeachment hoax died right there.”

Mr. Zelensky has said multiple times that he is ready to work with whoever wins the U.S. presidential election in November. “If Mr. Donald Trump becomes president, then we will work with him,” he said at a news conference this summer. “I am not afraid of it.”

Ukrainian officials started building bridges with Mr. Trump’s camp this year, hoping to shape his views on Ukraine in case he is elected. A group of Ukrainian lawmakers met with former Trump administration officials in March.

But as the U.S. election nears, Ukrainian officials have grown increasingly concerned about Mr. Trump’s claims that he would end the war swiftly if re-elected, fearing this could result in Ukraine being forced to cede significant territory to Russia.

Breaking with his self-professed neutrality, Mr. Zelensky questioned Mr. Trump’s plan to end the war in a recent interview with The New Yorker. He also described Mr. Trump’s running mate, Senator JD Vance of Ohio, who has been deeply critical of previous U.S. aid packages for Ukraine, as “too radical.”

“My feeling is that Trump doesn’t really know how to stop the war even if he might think he knows how,” Mr. Zelensky said in the interview. “With this war, oftentimes, the deeper you look at it, the less you understand.”

Mr. Zelensky’s comments to the magazine infuriated the Trump team — so much that the Trump Tower meeting almost didn’t happen.

Trump allies were also angry about a visit Mr. Zelensky made on Tuesday to a factory in Pennsylvania that supplies munitions for the war. Some close to Mr. Trump claimed that the appearance was “election interference” because Mr. Zelensky had posed for photos with prominent Democrats in the battleground state.

The fury in Mr. Trump’s orbit became so hot that Representative James Comer of Kentucky, the Republican chairman of the House Oversight and Accountability Committee, began an inquiry on Wednesday into Mr. Zelensky’s trip to Pennsylvania, implying that it was an improper campaign stop on behalf of Ms. Harris.

The House speaker, Mike Johnson, released an extraordinary public statement calling on Mr. Zelensky to fire his ambassador to the United States. The ambassador, Oksana Markarova, did not attend Friday’s meeting.

At a campaign event on Wednesday, Mr. Trump criticized Mr. Zelensky for being someone who “refuses to make a deal” with Russia despite the devastation in the country. Mr. Trump said that Mr. Zelensky was “making little nasty aspersions” toward him.

Still, Mr. Trump did not go as far in attacking Mr. Zelensky as some of his more anti-Ukraine allies had wanted. At least one adviser tried to rile up Mr. Trump about how Mr. Zelensky was effectively campaigning for Democrats, but the former president dismissed the suggestion, saying that he didn’t want to talk about it, according to a person with direct knowledge of the conversation who spoke on the condition of anonymity.

Mr. Zelensky sent a warm personal note to Mr. Trump to try to get the relationship back on track, telling him it was “important for us to have a personal contact and to understand each other 100 percent.”

After receiving the note, Mr. Trump agreed to meet with Mr. Zelensky, but he also posted the private message on his social media website, Truth Social, on Thursday. The former president has a history of publicizing private communications when he thinks they are politically advantageous. In this case, the message showed that it was Mr. Zelensky who sought the meeting.

Analysts in Ukraine say the Zelensky administration has been developing strategies to appeal to Mr. Trump’s key stated interests, such as shoring up the American economy. Some analysts there take comfort in the fact that after Russia illegally annexed Crimea in 2014, Mr. Trump reversed President Barack Obama’s policy of not providing lethal weapons to Ukraine. They were also encouraged to see Mr. Trump soft-pedal his opposition to additional American aid to Ukraine, giving Republican members of Congress the breathing room to vote in favor of the military package after months of holding back.

At the meeting on Friday, Mr. Trump sat at the center of the table, framed by American flags. There was no Ukrainian flag, an exclusion that would be out of the norm if it were an official state visit.

Several critical Trump advisers were also present. Richard Grenell, Mr. Trump’s former acting director of national intelligence, attended. Mr. Trump’s top political advisers, Susie Wiles and Chris LaCivita, sat at the conference table to Mr. Trump’s left. Mr. Zelensky brought his closest aide, his chief of staff, Andriy Yermak.

Mr. Trump said in the Fox News interview that he “learned a lot” in the meeting. He said he was open to meeting again, and Mr. Zelensky took the opportunity to invite Mr. Trump to visit Ukraine.

“I will,” Mr. Trump said.

In a post on X, Mr. Zelensky described the meeting as “very productive.”

“I presented him our Victory Plan, and we thoroughly reviewed the situation in Ukraine and the consequences of the war for our people,” Mr. Zelensky wrote in the post. “Many details were discussed. I am grateful for this meeting. A just peace is needed. We share the common view that the war in Ukraine must be stopped. Putin cannot win. Ukrainians must prevail.”

Mr. Zelensky’s final assertion — that Ukraine must prevail and Mr. Putin must be denied a victory — goes further than anything Mr. Trump has said in public.

Michael Gold contributed reporting.

Like Mr. Trump, Mr. Adams has repeatedly bashed the press coverage he has received since he took office. “We have to tell our news publications: Enough, enough, enough,” said Mr. Adams, who is a former police officer and the city’s second Black mayor and who created his own newsletter to circumvent the local media covering him, in late 2022.

Both try to demonstrate what Mr. Adams has called “swagger,” a macho patina of toughness. Both have projected law-and-order strength while surrounding themselves with people under legal scrutiny of their own.

And both have insisted they’re victims of political efforts to prosecute them for their stances on issues, prosecutions that they insist are the real corruption, not their own actions.

Mr. Adams will now test how far he can take the Trump playbook in seeking to remain in office. It remains to be seen whether the forces of political gravity that usually come with an indictment will drag him down. Mr. Trump will face a similar test in less than six weeks of whether his criminal travails will prevent him from winning the presidential election despite broad support within his party.

Mr. Trump was raised in Queens but nurtured on the Brooklyn political-machine relationships that his father, a successful real estate developer, had forged to help make building projects happen. Mr. Adams came through a different iteration of the Brooklyn machine, one that formed from an emerging Black political power base.

In both cases, they have been shape-shifters. Mr. Trump is a Republican-turned-Democrat-turned-independent-turned-Republican who once favored universal health care and was later slow to disavow support from the white supremacist David Duke. Mr. Adams is a Democrat-turned-Republican-turned-Democrat who had been under investigation previously and who admired Louis Farrakhan, the leader of the Nation of Islam, who has promoted antisemitism.

Both have been avatars of transactional politics, willing to assume different positions from what they held before, letting business elites and political centrists see them as bulwarks against what those elites viewed as creeping progressivism.

One Democratic strategist working in New York politics, granted anonymity to speak candidly about the circumstances surrounding both men, asked sarcastically which was more worrisome to their backers: Progressivism or corruption?

Mr. Trump on Thursday gave himself a platform on the Adams case, inadvertently or not. The indictment against the mayor was announced shortly before Mr. Trump, himself convicted of falsifying records to cover up a sex scandal and indicted three other times, held a news conference in Trump Tower.

For Mr. Adams, election to New York City’s highest office — a powerful role often described as the second-toughest job in America, rivaling the presidency — came a year after the city was an epicenter of the coronavirus, of Black Lives Matter protests that sometimes erupted into violence, of crime spikes amid pandemic shutdowns.

The Democratic Party was pitted against itself with candidates who had staked out deeply liberal positions on a range of issues, particularly policing, and Mr. Adams was seen by centrists, some Republicans and the city’s business interests as an antidote. It took until the end of his first year in office for the mayor’s image as the new face of the Democratic Party to start to fray.

For his part, Mr. Trump left office after his efforts to cling to power culminated in an attack on the Capitol by a pro-Trump mob. His popularity among the Republican base in the aftermath never eroded to the extent that many Washington hoped it would. The four times Mr. Trump was indicted in 2023, in the span of a few months, merely made him politically stronger within his party.

This week, Mr. Trump’s advisers were privately delighted that there was another public official facing a corruption indictment, creating a news story about legal travails that didn’t involve the former president and giving him an opportunity to claim that the system was corrupt.

That the Justice Department is going after him for political reasons has been a constant refrain of Mr. Trump’s for more than two years. Mr. Adams has said versions of the same thing, suggesting that the investigative focus on him is racist.

And while there have been some calls for Mr. Adams to resign, many Democrats are either averting their gazes or offering muted criticisms. It is not the full-throated defense that Mr. Trump has received from elected officials in his own party, but it is still different than what might have existed years ago for a scandal-tainted mayor.

One of the most vocal defenses of Mr. Adams came, not surprisingly, from Mr. Trump.

Mr. Trump defended Mr. Adams at his own news conference on Thursday, baselessly insisting that the mayor was indicted because he blasted the Biden administration over the migrant crisis that had strained city services, another refrain similar to Mr. Trump’s own political messaging. But Mr. Trump also conceded that he didn’t really know what the mayor had done and refused to acknowledge a question repeatedly asked by reporters about whether he would pardon the mayor if he returned to the White House.

“I will say this: I watched, about a year ago, when he talked about how the illegal migrants are hurting our city and the federal government should pay us, and we shouldn’t have to take them,” he said. “And I said, You know what? He’ll be indicted within a year. And I was exactly right, because that’s what we have. I said that he will be indicted because he did that. You take a look, that’s what they do. These are dirty players. These are bad people. They cheat and they do anything necessary. These are bad people.”

“I wish him luck,” Mr. Trump added.