Pete Hegseth, President-elect Donald Trump's pick for defense secretary, was back on Capitol Hill Tuesday looking to shore up support as he fends off new allegations of misconduct and sexual impropriety.

The allegations were top of mind for Republican senators, one of whom called recent reports "very disturbing." Several GOP lawmakers suggested Hegseth needed to come forward and address them.

But Hegseth, holding hands with his wife as he walked the halls, continued to ignore questions about the New Yorker report that he was forced to step down from two veteran nonprofit groups -- Veterans for Freedom and Concerned Veterans for America -- amid accusations of financial mismanagement, sexist behavior and other disqualifying behavior.

The magazine cited what it called a detailed seven-page whistleblower report -- compiled by multiple former C.V.A. employees -- stating that, at one point, Hegseth had to be restrained while drunk from joining the dancers on the stage of a Louisiana strip club, where he had brought his team. The report also says that Hegseth, who was married at the time, and other members of his management team sexually pursued the organization’s female staffers, the magazine said.

ABC News has not independently confirmed the magazine's account. Hegseth's attorney, Tim Parlatore, told The New Yorker the claims were "outlandish."

"We're going to meet with every senator that wants to meet with us, across the board, and we welcome their advice as we go through the advice and consent process," Hegseth told reporters as he arrived for a second day of sitdowns with senators.

Hegseth was asked dozens of questions by reporters, including what he would say to those troubled by the allegations, whether the women who've spoken out are lying, whether he had a drinking problem and if the Trump transition team had been aware of the allegations.

He did not respond, including when asked by ABC's Elizabeth Schulze about GOP Sen. Joni Ernst saying she thinks he should have agreed to a background check.

Trump's team came out in defense of Hegseth earlier Tuesday. Senior adviser Jason Miller, in an interview on CNN, attempted to brush off the allegations as "innuendo and gossip."

"So, when it comes to Pete Hegseth, there aren't any concerns, and we feel very good about his positioning for being confirmed by the Senate," Miller said. "Now we have to take the process very seriously."

Republican senators, peppered with questions on Hegseth and other recent Trump picks as they returned to Washington this week, also say they want a "normal" confirmation process to play -- which would routinely include FBI background checks.

But some of their statements, so far, stopped short of glowing endorsements.

"I think some of these articles are very disturbing. He obviously has a chance to defend himself here, but some of this stuff is -- it's going to be difficult. Time will tell,” said Sen. Lindsey Graham, who sits on the Senate Judiciary Committee.

"Leadership comes from the top, and I want to make sure that every young woman who joins the military space is respected," Graham said, seemingly referencing Hegseth's comments against women serving in combat roles.

Sen. Josh Hawley, another member of the key panel, argued Hegseth would have the opportunity to answer all questions during the confirmation process though notably indicated some of his Republican colleagues are "very worried."

"I would just urge my Republican colleagues, who are very worried, I know a number of them are expressing public concern -- it's fine, but I would just urge them, before they make up their minds, right before they make up their minds, let them have this hearing and listen to let's go through the process here and give them a shot to answer this and more and to lay out this vision for you," Hawley said.

Sen. Tommy Tuberville, who stood by Hegseth as a "great" pick on Monday, had similarly suggested Hegseth could face headwinds.

"Obviously, if it's to a certain degree, people are not going to vote to confirm it," Tuberville said when asked about the allegations after their meeting. "But what I know when I talk to him about what I've read, what I've studied and been around him, I'll vote for him."

Many suggesting that he needs to come forward and address it.

"Well, these allegations that have come up just in the last 12 to 14 hours are a surprise to all of us, and so yes, he does need to address those because this was not something of which we were aware, nor was President Trump aware of them," said Sen. Cynthia Lummis, R-Wyo., who met with Hegseth on Monday night with a group of senators.

Asked about his ability to make it through the nomination process, Lummis said she hopes to meet with him one-on-one and deferred to how he addresses the new allegations.

"It depends on how he addresses the issues that have been raised," Lummis said. "Some of the earlier issues that were raised about an incident in California I think were satisfactorily addressed and would not have interfered with his nomination, but some new things that have come to light in the last 12 to 14 hours are things he needs to address."

"I have read all the articles, I have seen all the allegations. And Mr. Hegseth is going to have to address it," Sen. John Kennedy, R-La., said.

"I want to know if they're true, and I want to hear his side of the story. And he's going to have to address them," Kennedy added.

Hegseth met Tuesday with Sen. Deb Fischer, one of two Republican women on the Senate Armed Services Committee, and GOP Sen. Bill Hagerty in their respective offices.

He was also scheduled to meet with Republican Sens. Ted Budd, Shelley Moore Capito, Jim Risch and Eric Schmitt.

Schmitt said he was "definitely going to ask questions" about the allegations.