She added that she had been contacted by other women who had complaints about sexual harassment at the network.

The abruptness of Mr. O’Reilly’s exit has created widespread uncertainty in the newsroom about the future of other executives, including Mr. Shine and Mr. Abernethy. But some people at Fox News said that it was unlikely that the Murdochs would allow a sense of capitulation to permeate the network and that keeping Mr. Shine and Mr. Abernethy in place would provide some needed stability at an anxious time.

Mr. Ailes and Mr. O’Reilly have denied the allegations of harassment.

Mr. O’Reilly’s ouster was a stunning reversal for 21st Century Fox, which had long stood by him even as allegations and settlements started to amass. Mr. O’Reilly, who started at Fox News in 1996, was considered the network’s top asset. His nightly program, “The O’Reilly Factor,” generated high ratings and pulled in hundreds of millions in advertising revenue.

But pressure mounted on the company to take action after a New York Times investigation early this month found that Mr. O’Reilly and the company had reached settlements with five women who had complained about sexual harassment or other inappropriate behavior by him. The agreements totaled about $13 million, the majority paid by him.

Earlier this year, the network extended Mr. O’Reilly’s contract by an additional four years. At the time, the company was aware of allegations of sexual harassment against him and had even reached two settlements involving such complaints. His previous contract had been set to expire this year.

But the new contract provided the company with some protections. Those included a provision that Mr. O’Reilly could be dismissed if the company was made aware of other allegations against him or if new ones arose, according to one person briefed on the matter. The contract also included provisions meant to get Mr. O’Reilly to address his behavior, the person said.