(Peter Stevenson/The Washington Post)

Bill O’Reilly’s tenure at Fox News became more imperiled Tuesday, with the lodging of a new harassment allegation against “The O’Reilly Factor” host and no apparent end in sight to the advertiser boycott that has undermined his program.

The board of Fox News’s parent company, 21st Century Fox, will meet Thursday, when O’Reilly’s fate could be determined, according to people close to the situation. Although the board has no direct vote over O’Reilly’s employment status, its members could be influential with the Murdoch family, which controls the company and would have the final say.

CNN reported that exit talks were underway between O’Reilly and Fox, but O’Reilly’s camp said such discussions haven’t taken place.

O’Reilly’s contract — signed in March — has an “opt out” clause that would require Fox to pay him a fixed amount if invoked, making extensive negotiations unlikely and unnecessary.

In the meantime, O’Reilly’s representatives seemed determined to put up a fight before it ever came to that. His attorney, Marc Kasowitz, issued two defiant statements Tuesday, both accusing “activists” and “far-left organizations” of ganging up on O’Reilly, one of the most popular personalities on cable TV.

Kasowitz — who has frequently represented President Trump in disputes with the news media — responded angrily after another woman alleged Tuesday that O’Reilly had subjected her to abusive treatment when she worked at the network.

The woman, who has remained anonymous, made a formal complaint to a Fox News hotline set up to field harassment allegations, according to her attorney, Lisa Bloom. She said O’Reilly had made disparaging racial and sexual comments to her while she was employed as a clerical worker at the network in 2008, Bloom said. The woman isn’t seeking compensation, just “accountability,” according to Bloom, who also represents Wendy Walsh, another O’Reilly accuser.

Bloom said she is working for Walsh and the former clerical worker on an unpaid basis and that neither of her clients is seeking monetary compensation.

Fox had no comment about the new allegation. But Kasowitz issued a statement saying, “It is outrageous that an allegation from an anonymous person about something that purportedly happened almost a decade ago is being treated as fact, especially where there is obviously an orchestrated campaign by activists and lawyers to destroy Mr. O’Reilly and enrich themselves through publicity-driven donations.”

Later Tuesday, Kasowitz issued a second statement. It read: “Bill O’Reilly has been subjected to a brutal campaign of character assassination that is unprecedented in post-McCarthyist America. This law firm has uncovered evidence that the smear campaign is being orchestrated by far-left organizations bent on destroying O’Reilly for political and financial reasons.”

The Murdochs — patriarch Rupert is the chairman of Fox News and sons James and Lachlan head 21st Century Fox — must decide whether O’Reilly is so badly damaged by the harassment complaints that his value to Fox is permanently diminished. Alternatively, they will have to assess whether getting rid of him would anger O’Reilly’s loyal viewers and perhaps deal a permanent blow to Fox, one of the most lucrative franchises in the family’s media empire.

Only a few weeks ago, either consideration seemed inconceivable. “The O’Reilly Factor,” which mixes discussion segments with the host’s famously pugnacious commentary, was performing better than it has in its 20-year history. The program drew an average of 4 million viewers each night during the first three months of the year, a record for the show and the most ever for a cable-news program. O’Reilly’s popularity, in turn, helped drive Fox News to record ratings and profits.

But in early April, the New York Times disclosed that O’Reilly and Fox had settled harassment complaints made by women he’d worked with at Fox over the years.

The newspaper found that O’Reilly and Fox had settled five such allegations since 2002, paying out about $13 million in exchange for the women’s silence. Two of the settlements, including one for $9 million in 2004, were widely reported. But the others had been kept secret by O’Reilly, Fox and the women involved.

In addition, Walsh — a former “O’Reilly Factor” guest — alleged that O’Reilly had harassed her in 2013. Walsh hasn’t sued or settled, and has spoken against O’Reilly repeatedly in recent weeks, drawing more negative attention to him and the network.

A law firm hired by Fox has investigated Walsh’s complaint and is expected to complete a confidential report about it before the parent company’s board ­meeting.

The intense media coverage surrounding O’Reilly led to a stampede of advertisers exiting O’Reilly’s program, leaving it almost without sponsorship over the past two-plus weeks. Various organizations, including the National Organization for Women, have called for O’Reilly’s firing, and intermittent protests have been held outside Fox News’s headquarters in New York.

The advertiser boycott has shown no signs of dissipating, even as O’Reilly has been off the program while on a two-week vacation. He is scheduled to return Monday, barring any decision about his future before then.