The company says it has discussed the issue with Mr. O’Reilly. It believes his new contract gives it more leverage over him regarding his behavior, according to two people familiar with the matter. Mr. O’Reilly has said that the allegations are without merit. He did not address the controversy on his show Monday night.

Earlier on Monday, Julie Roginsky, a current Fox News contributor, filed a lawsuit against Mr. Ailes, Fox News and Bill Shine, the network’s co-president, asserting that she faced retaliation for rebuffing Mr. Ailes’s sexual advances and for refusing to disparage Gretchen Carlson, the former Fox News host who sued Mr. Ailes last summer.

And a former regular guest on Mr. O’Reilly’s program, Wendy Walsh, who had recounted her allegations against him to The Times, held a news conference with her lawyer to discuss those claims and to call for an independent inquiry into sexual harassment at the network.

Also, the United States attorney’s office in Manhattan is investigating Fox News, including how it structured settlements.

On Monday, Fox News moved to contain the fallout from the weekend’s developments, urging its employees in an internal memo to report inappropriate behavior to the human resources department or other network executives. “Particularly in light of some of the accounts published over the last few days, I wanted to re-emphasize the message we have been conveying at our training sessions for several months,” said Kevin Lord, the network’s new head of human resources, who was hired in the aftermath of the Ailes scandal.

Irena Briganti, a Fox News spokeswoman, declined to comment on advertising decisions, Ms. Roginsky’s lawsuit or Ms. Walsh’s news conference.

Ms. Walsh, speaking in Los Angeles, repeated the account she provided to The Times. She said that Mr. O’Reilly did not follow through on a verbal offer to make her a contributor to his show after she declined an invitation to go to his hotel suite after a 2013 dinner in Los Angeles that was arranged by his secretary. She has not received a settlement and said she does not want any money. She did not report her complaints to Fox News at the time, she said, because she did not want to jeopardize her career prospects.