A former Fox News anchor who accused Bill O'Reilly of sexual harassment has claimed President Donald Trump tried to kiss her on the lips around the same time he married First Lady Melania Trump.

Juliet Huddy says the incident happened when they were in an elevator together at Trump Tower in New York back in "2005 or 2006".

At the time the billionaire tycoon, who married Melania in January 2005, was hosting The Apprentice on NBC.

"He took me to lunch at Trump Tower, just us two," she said on the Mornin' With Bill Schulz show on Thursday (7 December).

"He said 'goodbye' to me in an elevator while his security guy was there, rather than kiss me on the cheek he leaned in to kiss me on the lips.

"I wasn't offended, I was kind of like, 'Oh my god'."

Huddy, whom Trump knew as a co-host of the weekend show Fox & Friends, said Trump then invited her and her friend both back to see The Apprentice set, "And everything was copacetic after that."

Huddy said at the time she "didn't feel threatened" and wasn't offended.

But she added: "Now I have matured I think I would say, 'Woah, no', but at the time I was younger and I was a little shocked. I thought maybe he didn't mean to do it, but I was kind of making excuses."

Huddy, who is now a host on WABC radio, said Trump later spoke about the kiss off camera when he was her guest another Fox News show.

"Trump was a guest and he came on stage. He said, to the audience and producers, not on camera, 'I tried hitting on her but she blew me off.' He was laughing," Huddy recalled.

After the story was picked up by the US media, Huddy later tweeted that the Trump anecdote was "true," but reiterated that she felt "neither threatened nor offended " by the elevator incident.

But she added that she is offended by Trump's comments on "other matters", understood to be referring to the President's views on former Fox News anchor Bill O'Reilly.

Huddy reportedly received a settlement from 21st Century Fox after filing a sexual harassment complaint against O'Reilly.

O'Reilly was fired earlier this year after the New York Times reported that Fox had spent tens-of-millions of dollars settling numerous sexual harassment lawsuits against him.

"When all the stuff came out about Bill O'Reilly, Donald Trump was one of the people who said, 'I don't believe this happened and I don't believe he did it,'" Huddy said.

"I was actually very disappointed in Trump, I thought, 'You know what, f*** you.' He [Trump] has met me a bunch of times and he knows I am not [a liar]."