"We performed oral sex on each other, we had vaginal sex, and we had anal sex. Each act was mutual and completely consensual," Matt Lauer said

Matt Lauer is denying the allegation that he raped his former NBC News colleague Brooke Nevils.

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In the letter, Lauer, who was fired in November 2017 due to Nevils’ complaint, said he stayed mostly silent for the past two years to protect his family. He now calls his silence “a mistake.”

“In a new book, it is alleged that an extramarital, but consensual, sexual encounter I have previously admitted having, was in fact an assault. It is categorically false, ignores the facts, and defies common sense,” he said. “I had an extramarital affair with Brooke Nevils in 2014. It began when she came to my hotel room very late one night in Sochi, Russia. We engaged in a variety of sexual acts. We performed oral sex on each other, we had vaginal sex, and we had anal sex. Each act was mutual and completely consensual.”

PEOPLE is out to Nevils for comment.

Lauer continued: “The story Brooke tells is filled with false details intended only to create the impression this was an abusive encounter. Nothing could be further from the truth. There was absolutely nothing aggressive about that encounter. Brooke did not do or say anything to object. She certainly did not cry. She was a fully enthusiastic and willing partner. At no time did she behave in a way that made it appear she was incapable of consent. She seemed to know exactly what she wanted to do. The only concern she expressed was that someone might see her leaving my room. She embraced me at the door as she left.”

Lauer, who recently finalized his divorce from longtime wife Annette Roque, acknowledged that the encounter was the beginning of his affair with Nevils and “the first of many sexual encounters between us over the next several months.”

“At no time, during or after her multiple visits to my apartment, did she express in words or actions any discomfort with being there, or with our affair,” he said. “She also went out of her way to see me several times in my dressing room at work, and on one of those occasions we had a sexual encounter. It showed terrible judgment on my part, but it was completely mutual and consensual.”

“Brooke now says that she was terrified about the control I had over her career and felt pressure to agree to our encounters after Sochi. But at no time during our relationship did Brooke work for me, the Today Show, or NBC News,” he continued. “She worked for Meredith Vieira (who had not worked for the Today Show in several years) in a completely different part of the network, and I had no role in reviewing Brooke’s work.”

Lauer admitted he ended the affair “poorly” and “simply stopped communicating” with Nevils.

“She admitted to NBC at the time she filed her complaint that she called me late at night while I was home with my family in an effort to rekindle the affair,” he alleged. “But I attempted to go back to my life and pretend as if nothing had happened. I understand how that must have made her feel. However, being upset or having second thoughts does not give anyone the right to make false accusations years later about an affair in which they fully and willingly participated.”

Lauer said that when he was first made aware of Nevils’ complaint, he was not told that she had claimed their encounter in Sochi was non-consensual, adding, “Had I been, I would have defended myself immediately.”

Lauer, who pointed out what he claims are “contradictions” in Nevils’ story, concluded by stating that he has “never assaulted anyone or forced anyone to have sex. Period.”

“The details I have written about here open deep wounds for my family. But they also lead to the truth,” he said. “For two years, the women with whom I had extramarital relationships have abandoned shared responsibility, and instead, shielded themselves from blame behind false allegations. They have avoided having to look a boyfriend, husband, or a child in the eye and say, ‘I cheated.’ They have done enormous damage in the process. And I will no longer provide them the shelter of my silence.”

Image zoom Charles Sykes/Invision/AP/REX/Shutterstock

Reps for Vieira and Farrow have not yet responded to PEOPLE’s requests for comment.

In a statement read on-air Wednesday on the Today show, NBC News said, “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.”

Catch and Kill is out Oct. 15.