The crowd of supporters in Saginaw County, which he narrowly lost four years ago, included Mike Rogers, the former Michigan congressman and the Republican candidate for Michigan’s open Senate seat, and Pete Hoekstra, the Michigan Republican Party chairman.

Mr. Trump reiterated his familiar false claim that he had won the 2020 election and made no acknowledgment of new evidence that was unsealed against him on Wednesday in the federal election subversion case. He also said his campaign was up in all polls in every swing state, while several public polls show close races and Vice President Kamala Harris leading narrowly in a number of battlegrounds.

Mr. Trump also mischaracterized the state of funding at the Federal Emergency Management Agency, saying that the Biden administration had stolen disaster-relief money allocated to the agency to give to housing for undocumented immigrants so they would vote for Democrats.

He cast electric cars as a threat to the auto industry, while at the same time praising Elon Musk, the Tesla chief executive who has endorsed his candidacy and featured him prominently on X, the Musk-owned social media platform.

Michigan was one of a handful of swing states where Mr. Trump and his allies tried to overturn his defeat in 2020 through a series of maneuvers that included breaching voting equipment and seeking to seat a set of fake presidential electors. Some of his supporters have been criminally charged in the state, where Mr. Trump was named as an unindicted co-conspirator this year.

Mr. Trump spent time in his speech taking satisfaction over his choice of running mate, Senator JD Vance of Ohio, whose debate performance this week was applauded by many.

“I drafted the best athlete,” Mr. Trump said of Mr. Vance. The audience — several thousand supporters at a recreation center at Saginaw Valley State University, roughly 100 miles north of Detroit — cheered.

And he mused, at one point, that instead of being on a beach in Monte Carlo or someplace else, he was running for the presidency again. “If I had my choice of being here with you today or being on some magnificent beach with the waves hitting me in the face, I would take you every single time.”

Overall as of Thursday, Ms. Harris led by two percentage points in Michigan, according to The New York Times’s polling average, 49 percent to 47 percent. The vice president is scheduled to return to the state on Friday, campaigning in Detroit and Flint.

Ms. Cheney said that, in November, putting patriotism ahead of partisanship should not merely be an aspiration — “it is our duty.”

Her remarks, delivered with an air of somber restraint, were as much a public indictment of Mr. Trump as they were an endorsement of Ms. Harris. Calling his candidacy “a threat unlike any we have faced before,” she called on conservatives to join her in an “urgent cause” to elect Ms. Harris and to reject what she called the former president’s “depraved cruelty.”

“I know that she will be a president who will defend the rule of law,” Ms. Cheney said of Ms. Harris, “and I know that she will be a president who can inspire all of our children and, if I might say so, especially our little girls.”

The joint appearance was one of the starkest examples to date of how Ms. Harris has endeavored to pitch herself as a unifying president who values pragmatism over partisanship. Her overarching goal is to win over moderate and independent voters who will be crucial to delivering her a decisive victory.

The event took place at Ripon College, where hundreds of people gathered on a lawn near the campus’s main building, which was adorned with American flags and posters that read: “Country over party.” At several points in the program, the crowd cheered, “Thank you, Liz” and “Ka-ma-la.”

Both women spoke about the significance of the site where the Republican Party’s founding leaders first met, bonding over their opposition to slavery. “Liz Cheney stands in the finest traditions of its leaders,” Ms. Harris said.

The vice president said that Ms. Cheney’s endorsement held “special significance,” and that while the two politicians might not agree on much, they shared a love of country and democratic ideals. Repeating her promise to be a president for all Americans regardless of party, Ms. Harris said she had sworn an oath to uphold the Constitution six times in her career.

“The president of the United States must not look at our country through the narrow lens of ideology or petty partisanship or self-interest,” Ms. Harris said. “The president of the United States must not look at our country as an instrument for their own ambitions. Our nation is not some spoil to be won. The United States of America is the greatest idea humanity ever devised.”

She added, “And so, in the face of those who would endanger our magnificent experiment, people of every party must stand together.”

Ms. Harris’s campaign has used Ms. Cheney’s endorsement, and those of a stream of other Republicans, in assailing Mr. Trump as a threat to the republic, and in blunting accusations by his campaign that the vice president is a “radical liberal.”

Mr. Trump responded in the early hours of Friday, writing on his social media site that Ms. Cheney was a “low IQ War Hawk” and that she and Ms. Harris were “a pathetic couple” who were “suffering gravely from Trump Derangement Syndrome.”

Steven Cheung, a Trump campaign spokesman, blasted the records of both women afterward. “The both of them are made for each other — proponents of endless wars, killers of Social Security, and enemies of American workers,” he said in a statement.

Ms. Harris’s campaign has sought to recast her political image as a left-leaning Californian by downplaying or abandoning some of the progressive positions she held when she first ran for president in the 2020 race. During this campaign, she has branded herself a “pragmatist” and a “capitalist,” and has spoken more openly about issues that appeal to the conservative base, like gun ownership. She has also suggested that she would appoint a Republican to her cabinet, if elected.

In a presidential race that may be won by razor-thin margins in November, Wisconsin appears to be a near tossup between Ms. Harris and Mr. Trump. President Biden won the state by only 20,600 votes in 2020, and a recent poll by The New York Times and Siena College showed Ms. Harris with 49 percent support among likely voters, versus Mr. Trump at 47 percent.

Ms. Harris’s decision to appear alongside Ms. Cheney, a Wisconsin native, signals that her campaign is hoping to appeal to Republican voters who have been repelled by Mr. Trump’s style of politics. The two women agree on little politically beyond their distaste for Mr. Trump. They had next to no relationship when they overlapped in Congress, though they did speak on the phone about Ms. Cheney’s decision to endorse the vice president.

Ms. Cheney was a onetime critic of Ms. Harris. In an August 2020 interview on Fox News, shortly after Mr. Biden chose her as his running mate, Ms. Cheney called Ms. Harris ’s voting record in the Senate “to the left of Bernie Sanders and Elizabeth Warren.” She added, “It’s very clear, she is a radical liberal.”

But after the Capitol attack, Ms. Cheney set partisan labels aside. She became the top Republican on the House committee that investigated Mr. Trump’s role in the riot. Suddenly an outcast in her party, she later lost her seat to a Trump-backed challenger.

Ms. Cheney’s appearance for Ms. Harris on Thursday was also striking because of the timing: On Wednesday, a 165-page brief from the special counsel, Jack Smith, laid out new evidence of how Mr. Trump tried to remain in power despite losing the 2020 election.

During her speech, Ms. Cheney brought up the fresh details, including Mr. Trump’s apparent nonchalance when he was implored to ensure the safety of his vice president, Mike Pence, whom rioters had threatened to hang on Jan. 6, 2021.

“So what?” the former president said, according to the brief.

Ms. Cheney told the crowd, “We have a responsibility, all of us, to remind people that our institutions don’t defend themselves.” She added, “We the people defend our institutions.”

Calling Mr. Trump “vindictive,” Ms. Cheney said “any person who would do these things can never be trusted with power.”

Ms. Cheney first said she planned to vote for Ms. Harris at a conference last month in North Carolina. It was a major step in a long turnabout for a staunchly conservative former lawmaker, who is pro-gun, anti-abortion and hawkish on national security issues.

Days later, her father, former Vice President Dick Cheney, said that he would also vote for Ms. Harris.

On Thursday, Ms. Cheney made clear that she had not strayed from her traditional, Republican bona fides. Her campaign work started at age 10, she said, when she helped seal envelopes for President Gerald Ford’s re-election campaign. She cast her first vote for a presidential race in 1984, she went on, and referred to herself as a Reagan Republican.

“I was a Republican even before Donald Trump started spray-tanning,” she jabbed.

Mr. Trump, for his part, held a rally on Thursday in Michigan, where Ms. Harris will campaign on Friday. During his speech, he continued to claim that he won the 2020 election.

Nicholas Nehamas and Reid J. Epstein contributed reporting from Washington.