Another of Fox News’s prime-time personalities has been accused of wrongdoing and is leaving, the latest setback in a season of tumult for the cable network.

Bob Beckel, a host of the 9 p.m. talk show “The Five,” was fired on Friday because of an insensitive remark he made to an African-American employee, Fox News said.

The network declined to elaborate on the specifics of Mr. Beckel’s remark, saying that the episode had been reported to the human resources department on Tuesday and then investigated.

A lawyer for the employee, an information-technology worker, provided a more detailed account. The lawyer, Douglas H. Wigdor, said on Friday that his client had been trying to service Mr. Beckel’s computer when Mr. Beckel stood up abruptly and walked out of his office, explaining that he was leaving because the employee was black.

Mr. Wigdor also represents 11 Fox News employees in a class-action racial discrimination suit against the network. (His law firm also represents plaintiffs in a racial discrimination suit against The New York Times).

Mr. Wigdor said that Mr. Beckel had tried to persuade his client to withdraw the complaint during a meeting with Fox News’s new executive vice president for human resources, Kevin Lord.

In a statement, Fox News disputed that account. “No one tried to persuade Mr. Wigdor’s client to withdraw his complaint,” a spokesperson wrote. The network said that Mr. Lord responded to the employee’s complaint within seven minutes of receiving it, and that Mr. Beckel apologized to the employee on Friday, shortly after learning of his dismissal.

Inquiries to Mr. Beckel were not returned on Friday.

Fox News has been reeling from the rapid-fire departures of marquee stars like Megyn Kelly and Bill O’Reilly, and a harassment and discrimination scandal that includes recent lawsuits alleging episodes of racial and gender bias and that shows few signs of abating.

The founding chairman of the network, Roger E. Ailes, died on Thursday, 10 months after he was forced out after he was accused of serial sexual harassment. One of the network’s co-presidents, Bill Shine, a longtime aide to Mr. Ailes, resigned under pressure this month, and his position has yet to be filled.

The drumbeat of tough headlines has taken a toll on newsroom morale, with employees on and off camera describing a feeling of being under siege. Mr. Ailes’s death, caused by complications from a fall last week at his home in Palm Beach, Fla., also came as a shock, The network’s anchors offered teary on-air tributes to him throughout Thursday, some acknowledging his flaws, while hailing skills and wiliness as a broadcaster.

This is not Mr. Beckel’s first acrimonious departure from Fox News. In 2015, Mr. Beckel, who is known for a folksy delivery and his signature suspenders, was dismissed from “The Five” and accused by Mr. Shine in a statement of taking “tremendous advantage of our generosity, empathy and good will.”

But Mr. Beckel returned to Fox News and “The Five” this year, with the network’s executive chairman, Rupert Murdoch, offering warm words about his new hire in a news release. Mr. Beckel and “The Five” moved to prime time this month, after a scheduling shuffle prompted by the firing of Mr. O’Reilly.

A onetime campaign manager for Walter Mondale, the 1984 Democratic presidential nominee, Mr. Beckel played the role of contrarian liberal among the mostly right-leaning group on “The Five.” His role will be filled, at least temporarily, by the political commentator Juan Williams, another regular on the show.