The public outcry, advertising boycott and federal inquiry were not the only issues weighing on the Murdochs. The bid for the Sky satellite company was a high priority for the elder Mr. Murdoch, an acquisition he considered important to his legacy.

Mr. O’Reilly’s settlements arose as an issue at an April 18 meeting between 21st Century Fox executives and the British regulators who were reviewing the company’s bid, according to a government report on the meeting. The report said regulators were “concerned that board members regarded Mr. O’Reilly’s settling cases personally as somehow a point in his favor.”

A day after the meeting with regulators, while Mr. O’Reilly was on vacation in Italy, he was dismissed. He left the network with a $25 million payout.

In a statement provided this past week, the company said: “21st Century Fox has taken concerted action to transform Fox News including installing new leaders, overhauling management and on-air talent, expanding training, and increasing the channels through which employees can report harassment or discrimination.” It added that “these changes come from the top.”

The company’s bid for Sky remains under regulatory scrutiny.

In response to questions from The Times, the company said that it had “complied fully” with document requests from the United States attorney’s office and that “it would be inappropriate to comment on a pending investigation other than to reiterate that we are cooperating fully.”

In recent weeks Mr. O’Reilly has made several public appearances to promote a new book. He said on the “Today” show that he never sent a lewd text or email to a Fox News employee, that his conscience is clear and that “a political and financial hit job” brought him down.

“This is horrible, it’s horrible what I went through, horrible what my family went through,” Mr. O’Reilly said in a raised voice at the end of the interview with The Times. “This is crap, and you know it.”