Former "Today" host Matt Lauer on Wednesday denied an allegation of sexual assault, speaking out at length for the first time since he was fired by NBC News in November 2017.

Former NBC News colleague Brooke Nevils told investigative journalist Ronan Farrow that Lauer raped her while the two were in Russia for the 2014 Sochi Olympics, according to a report in Variety. The allegation is part of an upcoming book from Farrow. NBC News has not seen a copy of the book.

Lauer, in a letter issued by his lawyer, Libby Locke of the law firm Clare Locke, confirmed he had a relationship with Nevils but said it was "completely consensual."

"In a new book, it is alleged that an extramarital, but consensual, sexual encounter I have previously admitted having, was in fact an assault," Lauer said in the letter. "It is categorically false, ignores the facts, and defies common sense."

Lauer also said Nevils mischaracterized their first sexual encounter. She told Farrow that Lauer anally raped her when she was inebriated and unable to consent, according to Variety, which says it has obtained a copy of the book. Nevils reportedly told Lauer repeatedly she did not want to have anal sex and that she cried during the encounter.

"It was nonconsensual in the sense that I was too drunk to consent," Nevils told Farrow, according to Variety. "It was nonconsensual in that I said, multiple times, that I didn’t want to have anal sex."

Lauer, who was on the "Today" show for two decades, was fired by NBC News within 24 hours of Nevils making a detailed complaint accusing him of inappropriate sexual behavior.

NBC News said in a statement issued after the Variety report, "Matt Lauer’s conduct was appalling, horrific and reprehensible, as we said at the time. That’s why he was fired within 24 hours of us first learning of the complaint. Our hearts break again for our colleague."

Lauer said in the letter that their encounter was consensual and that Nevils was a "willing partner."

"Brooke did not do or say anything to object," Lauer said. "She certainly did not cry."

Nevils did not immediately respond to requests for comment.

Lauer went on to detail his relationship with Nevils, which he said continued after Sochi for several months. Lauer said he had a sexual encounter with Nevils in his dressing room, which he said "showed terrible judgment on my part..."

She did acknowledge in Farrow's book that she had subsequent sexual encounters with Lauer, but said she was fearful over how Lauer could hurt her career.

"This is what I blame myself most for,'" she told Farrow, according to Variety. "It was completely transactional. It was not a relationship."

Lauer also questioned Nevils' motive for coming forward, stating that she had sought anonymity while also pursuing a monetary payment from NBC and seeking to write a book. NBC News has not confirmed that Nevils sought a book deal. Farrow reported that Nevils did not seek payment before going on medical leave in 2018 but did eventually accept a seven-figure settlement, according to Variety.

Lauer said people who were familiar with his relationship with Nevils had reached out to him "and shared what they know."

He said he hoped those people would speak publicly.

"I hope those people will understand that these allegations cross a serious line, and what they can share is a vital truth, even if it may seem unpopular," Lauer said.