WASHINGTON — Donald Trump's embattled nominee for defense secretary says he still has the president-elect's backing after reports suggested his nomination may be in jeopardy over allegations of misconduct.

Trump is considering replacing Pete Hegseth with Florida Governor Ron DeSantis, the BBC's partner CBS News reported after Hegseth's nomination came under intense scrutiny.

Since Trump nominated the former Fox News host, questions about Hegseth's qualifications have been raised - and a past sexual assault allegation has surfaced.

Hegseth has denied any wrongdoing, and was never arrested or charged.

Hegseth, on Wednesday, did not address the DeSantis reports directly and told reporters that Trump had told him to "keep going, keep fighting".

He spent most of the day in closed-door meetings on Capitol Hill, seeking to quell concerns and shore up support in the Senate.

“I spoke to the president this morning. (Trump) supports me fully. We’re not going anywhere,” Hegseth told the BBC, stopping to speak outside the Senate chamber.

In a post on X on Wednesday morning, Hegseth accused "the Left" of trying to smear him with "fake" stories.

But his nomination is also the subject of growing scrutiny by members of his own party - including US senators who have the power to confirm or deny his appointment when asked to vote on it.

"I think some of these articles are very disturbing," Republican Senator Lindsey Graham told CBS on Tuesday. "He obviously has a chance to defend himself here, but some of this stuff is going to be difficult."

"The president gets the benefit of the doubt with his nominees," fellow Republican Senator Mike Rounds of South Dakota told the BBC. "But we still have a role to play. We’ll ask him questions and we’ll go from there.”

Other Republicans signalled that they supported Hegseth despite the controversies.

Senator Rick Scott of Florida said he believed Hegseth would receive a Senate confirmation. He told reporters that Hegseth was "somebody that's clearly smart, and he's somebody that clearly wants to make changes."

DeSantis, who was elected Florida governor in 2018, did not reply to a request for comment. A spokesperson for Trump declined to say whether DeSantis was under consideration for the post.

DeSantis ran against Trump in the Republican primary, and before dropping out, he was considered by some to be "Trump 2.0" - a Republican who could deliver Trump's populist agenda without the baggage.

The latest speculation - first reported by the Wall Street Journal - comes as Hegseth meets members of Congress this week to discuss the job and drum up support.

Jasmine Crockett, a House Democrat from Texas and vocal Trump critic, does not view DeSantis as a better choice.

Like Hegseth, Crockett says DeSantis will "continue the culture war issues" he battled as Florida governor that could hinder the military's "problem with recruitment".

A graduate of Princeton and Harvard universities, Hegseth was an infantry platoon leader in Guantanamo Bay and Iraq, and was awarded the Bronze Star Medal.

In nominating Hegseth, who is also a former Fox News TV host, Trump highlighted the former soldier's education, and his military experience in Afghanistan and Iraq.

"With Pete at the helm, America’s enemies are on notice - our military will be great again, and America will never back down," Trump wrote.

But even as a veteran of the wars in Afghanistan and Iraq, the 44-year-old does not have the extensive experience typical for the cabinet position. He also would be the second-youngest person to serve in the office.

In addition, since his nomination, a police report detailing accusations of an alleged sexual assault in 2017 has surfaced.

The woman quoted in the complaint said that Hegseth, then a Fox host, took her phone and blocked the door to a hotel room while at a Republican conference in California.

Hegseth denies any wrongdoing, saying the encounter was consensual.

In an interview published Wednesday, conservative journalist Megyn Kelly asked Hegseth if he had assaulted a woman in Monterey, California, in 2017.

"Absolutely not," he replied.

His mother, Penelope Hegseth, defended her son on the Fox and Friends program on Wednesday morning after the New York Times published details of an email she wrote to him in 2018, accusing him of routinely mistreating women.

"I wrote that in haste. I wrote that with deep emotions," she said of the email, adding that her son and his first wife were "going through a very difficult divorce".

"He's redeemed, forgiven, changed. I think we all are after seven years," she said.

In addition to the accusations, some of Hegseth's past comments about how he might change the defense department have also raised eyebrows.

On a recent podcast, Hegseth said the chairman of the joint chiefs of staff - the top military leader in the US - should be fired, along with any military leader "involved in any of the DEI [diversity, equity and inclusion] woke [expletive]".

He also has argued that women should not serve in combat roles because this practice had not made the military "more effective" or "more lethal".

"As we think about his comments that talk about DEI, it's yet another disqualifying attribute that he has," Representative Marilyn Strickland, a Democrat on the House Armed Services Committee, told the BBC.

There is increasing scepticism about Hegseth's chances of getting enough votes to be confirmed by the Senate, CBS reports.

At least four Republican senators would be likely to vote against him if they voted today, two sources told the news outlet.

Republicans are expected to have a three-seat majority in the Senate, with 53 out of 100 senators, which must confirm cabinet-level positions in Trump's new team. Losing four Republican votes would be enough to sink Hegseth's nomination, provided Democrats and independents also vote against him.

Hegseth is not Trump's first controversial nomination before he returns to the White House.

Former Florida Congressman Matt Gaetz, who Trump nominated for US attorney general, also faced scrutiny over allegations of sexual misconduct - which he denied - that were the subject of a congressional report.

Gaetz eventually withdrew his nomination in late November, saying that the controversy against him "was unfairly becoming a distraction" from the work of the incoming Trump administration. — BBC