Last January, six months after Fox News ousted its chairman amid a sexual harassment scandal, the network’s top-rated host at the time, Bill O’Reilly, struck a $32 mi .llion agreement with a longtime network analyst to settle new sexual harassment allegations, according to two people briefed on the matter — an extraordinarily large amount for such cases.

Although the deal has not been previously made public, the network’s parent company, 21st Century Fox, acknowledges that it was aware of the woman’s complaints about Mr. O’Reilly. They included allegations of repeated harassment, a nonconsensual sexual relationship and the sending of gay pornography and other sexually explicit material to her, according to the people briefed on the matter.

It was at least the sixth agreement — and by far the largest — made by either Mr. O’Reilly or the company to settle harassment allegations against him. Despite that record, 21st Century Fox began contract negotiations with Mr. O’Reilly, and in February granted him a four-year extension that paid $25 million a year.

Interviews with people familiar with the settlement, and documents obtained by The New York Times, show how the company tried and ultimately failed to contain the second wave of a sexual harassment crisis that initially burst into public view the previous summer and cost the Fox News chairman, Roger Ailes, and eventually Mr. O’Reilly, their jobs.

In January, the reporting shows, Rupert Murdoch and his sons, Lachlan and James, the top executives at 21st Century Fox, made a business calculation to stand by Mr. O’Reilly despite his most recent, and potentially most explosive, harassment dispute.

Their decision came as the company was trying to convince its employees, its board and the public that it had cleaned up the network’s workplace culture. At the same time, they were determined to hold on to Mr. O’Reilly, whose value to the network increased after the departure of another prominent host, Megyn Kelly.

Lis Wiehl, a former Fox News legal analyst, in 2013. She appeared regularly on Mr. O’Reilly’s show for 15 years. Taylor Hill/Getty Images

But by April, the Murdochs decided to jettison Mr. O’Reilly as some of the settlements became public and posed a significant threat to their business empire.

Early that month, The Times reported on five settlements involving Mr. O’Reilly, leading advertisers to boycott his show and spawning protests calling for his ouster. About the same time, the O’Reilly settlements arose as an issue in 21st Century Fox’s attempt to buy the European satellite company Sky.

In addition, federal prosecutors who had been investigating the network’s handling of sexual harassment complaints against Mr. Ailes had asked for material related to allegations involving Mr. O’Reilly, according to an internal Fox email obtained by The Times.

“Their legal theory has been that we hid the fact that we had a problem with Roger,” Gerson Zweifach, Fox’s general counsel, wrote in the email, referring to the prosecutors and Mr. Ailes, “and now it will be applied to O’Reilly, and they will insist on full knowledge of all complaints about O’Reilly’s behavior in the workplace, regardless of who settled them.”

He warned the Murdochs that they should expect details from the January settlement to become public. Six days later, Mr. O’Reilly was fired.

In a statement, 21st Century Fox said it was not privy to the amount of the settlement and regarded Mr. O’Reilly’s January settlement, which was reached with a 15-year Fox News analyst named Lis Wiehl, as a personal issue between the two of them.

Regarding Mr. O’Reilly’s contract extension, the company said Fox News “surely would have wanted to renew” Mr. O’Reilly’s contract, noting that “he was the biggest star in cable TV.”

It emphasized that provisions were added to the new contract that allowed for his dismissal if new allegations or other relevant information arose. “The company subsequently acted based on the terms of this contract,” the statement said.

In an interview on Wednesday, Mr. O’Reilly, at times combative and defiant, said there was no merit to any of the allegations against him. “I never mistreated anyone,” he said, adding that he had resolved matters privately because he wanted to protect his children from the publicity.

“It’s politically and financially motivated,” he said of the public outcry over the allegations against him, “and we can prove it with shocking information, but I’m not going to sit here in a courtroom for a year and a half and let my kids get beaten up every single day of their lives by a tabloid press that would sit there, and you know it.”

He declined to specifically address questions about the settlement with Ms. Wiehl or any others.

Mr. O’Reilly’s lawyer, Fredric S. Newman, described his client’s relationship with Ms. Wiehl as an 18-year friendship in which she at times gave him legal advice.

Asked about the allegation of a nonconsensual sexual relationship, a representative for Mr. O’Reilly, Mark Fabiani, said that 21st Century Fox was “well aware” Ms. Wiehl had signed a sworn affidavit “renouncing all allegations against him,” adding that after receiving the document Fox News offered Mr. O’Reilly “a record breaking contract.”