Former TV producer Brook Nevils alleges the attack in Catch and Kill, by investigative journalist Ronan Farrow.
Mr Farrow writes that Mr Lauer invited Ms Nevils to his room where he forcibly kissed and raped her.
Mr Lauer who lost his job in November 2017 called the allegations “dangerous and defamatory“.
Farrow’s new book Catch and Kill details a new claim from Ms Nevils, the previously unnamed former NBC News employee whose complaint led to Mr Lauer getting fired from NBC’s morning show Today.
Ms Nevils says that when they were covering the 2014 Sochi Winter Olympics in Russia, Mr Lauer invited her to his hotel room after a night of drinks.
Once in the suite, she says, he pushed her against the door and kissed her.
She says he shoved her on to the bed and anally raped her.
She said: “It was nonconsensual in that I said, multiple times, that I didn’t want to have anal sex.”
Her sexual encounters with Mr Lauer continued when they both returned to New York.
“This is what I blame myself most for,” Ms Nevils said.
“It was completely transactional. It was not a relationship.”
In a lengthy letter issued by his lawyer to Variety, Mr Lauer said he has refrained from speaking out until now on such “false and salacious allegations” in order to protect his children.
He rubbished the claim as “part of a promotional effort to sell a book”.
He continued: “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.”