Democratic Lt. Gov. Justin Fairfax of Virginia strongly denied an uncorroborated sexual assault allegation first published by a conservative website, calling the accusation a "smear" and "character assassination." His remarks Monday afternoon come as many Democrats are calling for Gov. Ralph Northam to resign over the revelation of racist yearbook photos from his time in medical school, which would elevate Fairfax to the governorship.

"I have lived my life in a way that I'm proud of," Fairfax told reporters in the rotunda of Virginia's state Capitol.

Fairfax's office later said the unsubstantiated allegation he assaulted a woman when he was young Democratic staffer in 2004 was "false" and threatened legal action against "people who continue to spread these false allegations."

Virginia Lt. Gov. Justin Fairfax, center, speaks to the media in the rotunda in front of the statue of George Washington at the Capitol in Richmond, Va., on Mon., Feb. 4, 2019. AP

On Sunday night, Big League Politics — a right-wing political site that first published the photo from Northam's yearbook, in which one man is wearing blackface and another is dressed as a member of the Ku Klux Klan — reported that a woman who is currently a fellow at Stanford University said a man sexually assaulted her at the 2004 Democratic National Convention.

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In an early morning statement, Fairfax's office denied the allegation and claimed The Washington Post had found "significant red flags and inconsistencies within the allegations" when it investigated the matter last year. The Post did confirm the woman contacted the newspaper after Fairfax's election to claim he had sexually assaulted her in 2004, but the paper refuted Fairfax's characterization of why it declined to publish a story about the accusation.

"The Post did not find 'significant red flags and inconsistencies within the allegations,' as the Fairfax statement incorrectly said," according to The Post's report Monday. Instead, The Post said it did not run the story because it "found no similar complaints of sexual misconduct against him" after talking with people from Fairfax's college, law school and political circles, and could not corroborate the woman's account. Fairfax told The Post the encounter had been consensual and had taken place before he was married.

In a statement late Monday afternoon, The Post's executive editor Marty Baron wrote, "Lt. Gov. Fairfax is a public official who may well rise to the position of governor. He began the morning by issuing a statement regarding allegations against him, making specific representations about Post reporting that had not resulted in publication. We then had an obligation to clarify the nature of both the allegations and our reporting."

When he spoke with reporters on Monday, Fairfax confirmed meeting the woman and having sexual activity with her that was "100 percent consensual," but he repeatedly and vehemently denied sexually assaulting her. Someone familiar with the situation told CBS News the woman reached out to Fairfax via email after their initial encounter and asked him to meet in New York City.

The 39-year-old Democrat called it suspicious that the allegation surfaced amid a time when he could possibly assume the governorship if Northam steps down. "Does anybody believe that's a coincidence?" Fairfax asked.

Ofirah Yheskel, a spokesperson for Northam's office, rejected rumors that people close to the governor were behind the allegation against Fairfax, calling them "absolutely untrue" in a statement to CBS News.

Patrick Howley, the founder of Big League Politics who wrote both articles on Northam and Fairfax, defended his reporting in an interview with CBSN on Monday. The former Breitbart News reporter declined to detail some of his sourcing, but said his "approach" to the stories was "unimpeachable."

"I'll see him in court," Howley said, referring to Fairfax's threat of legal action.

Asked if Northam should relinquish his post, Fairfax said the governor has to make a decision that's in the best interest of Virginia, again declining to call for Northam's resignation.

Ed O'Keefe, Jack Turman and Nicole Sganga contributed to this report.