Pressure mounted on Tuesday for Fox News to take action against its top-rated host, Bill O’Reilly, as a series of prominent companies pulled advertising from his show and a leading women’s rights group called for his ouster.

Following an investigation by The New York Times over the weekend that revealed multiple settlements over allegations of sexual harassment or other inappropriate behavior by Mr. O’Reilly, the network faced a major advertising revolt as more than a dozen marketers said that they were withdrawing their ads from “The O’Reilly Factor.” Escalating the tension, the National Organization for Women called for Mr. O’Reilly to be fired and said an independent investigation should be conducted into the culture at Fox News.

“Fox News is too big and too influential to simply let this go,” Terry O’Neill, the president of NOW, said in a statement.

And inside Fox News, three women who work in the newsroom said that the continued support of Mr. O’Reilly by Fox News and its parent company, 21st Century Fox, led them to question whether the company was committed to maintaining a work environment “based on trust and respect,” as executives had promised last summer after the network’s founding chairman, Roger E. Ailes, was ousted. The employees requested anonymity because they feared retaliation for speaking publicly.