Swirling tensions at Fox News burst into public view on Thursday as one of its stars, Sean Hannity, spoke out in defense of an embattled executive at the center of an expanding culture clash inside the network.

In an extraordinary series of Twitter posts, Mr. Hannity seemed to yoke himself to the fate of the executive, Bill Shine, a behind-the-scenes fixer who rose to become the network’s co-president after its former chairman, Roger Ailes, was ousted last summer.

Mr. Hannity was referring to a report in New York magazine by Gabriel Sherman that Mr. Shine’s support from the Murdoch family, which controls Fox News Channel, was wavering.

If Mr. Shine were removed, Mr. Hannity wrote to his 2.3 million followers, “That’s the total end of the F.N.C. as we know it. Done.”

It is unusual for a television anchor to weigh in publicly on sensitive internal matters at a network. But Mr. Shine’s job security has been a matter of intense speculation inside Fox News’s Manhattan newsroom, which is still reeling from the forced exit of Bill O’Reilly in the wake of revelations that Mr. O’Reilly and Fox News had paid millions to settle accusations of harassment.

Mr. Shine was a loyal lieutenant to Mr. Ailes, and his continued role in newsroom leadership has been cited by women’s groups and some newsroom employees as a sign that Fox News’s parent company, 21st Century Fox, is not serious about reforming the workplace culture embodied by Mr. Ailes and Mr. O’Reilly.

Mr. Shine has been cited in at least four lawsuits against the network brought by current or former employees. Among the accusations are claims that Mr. Shine ignored or dismissed concerns about harassment, enabled or concealed Mr. Ailes’s harassment and, in one instance, made racially charged remarks.

Mr. Shine has denied all wrongdoing.

A spokesman for 21st Century Fox declined to comment on Thursday. But Rupert Murdoch, its executive chairman, went to lunch this week with Mr. Shine and Fox News’s other co-president, Jack Abernethy, at a prominent restaurant on Central Park South, which was widely seen as a sign of support.

Mr. Shine was not in the office on Thursday, and he was not scheduled to work on Friday, raising concern among his friends. Both days off were previously planned, a Fox News spokeswoman said.

An affable Long Island commuter who eschews the glamour of the television world, Mr. Shine also has strong supporters at Fox News, including some of the network’s top personalities. Mr. Hannity, who posted “#IStandWithShine” on Twitter on Thursday, is perhaps his staunchest ally, a longtime friend who brought Mr. Shine to Fox News in the 1990s after they met working in talk radio on Long Island.

Mr. Shine has not been publicly accused of the sort of aggressive harassment or coercion that was repeatedly attributed to Mr. Ailes and Mr. O’Reilly. (Both have denied wrongdoing.) Several current and former employees who worked closely with Mr. Shine, granted anonymity to speak freely about the network, said they knew of no episodes in which he had treated women poorly.

Still, in recent days Mr. Shine has expressed deep anxiety about his position at the network, according to several people who have spoken with him. New York magazine reported early Thursday that Mr. Shine had requested a show of public support from Rupert Murdoch’s sons, Lachlan and James. Representatives of Fox News and the Murdoch family said Mr. Shine had not directly approached the sons about a statement.

Mr. Shine is not alone in wondering about more senior-level departures. Some Fox News employees have speculated that the Murdoch family’s decision to fire Mr. O’Reilly was a signal that the old-guard, Ailes-era management of Fox News is on the way out.

Several employees said that one sentiment heard in the newsroom is that if the network could fire Mr. O’Reilly — its highest-rated anchor and a source of tens of millions of dollars in annual revenue — then no employee was safe. Several other executives who worked closely with Mr. Ailes, including Suzanne Scott, the programming chief, and Dianne Brandi, the general counsel, also remain at Fox News.

When the Murdochs moved swiftly this month to remove Mr. O’Reilly, they were motivated in part by concerns over an advertising boycott, an internal investigation into his behavior and the potential effect of the O’Reilly scandal on a pending acquisition attempt in Europe.

Fox News, which remains the dominant brand in cable news, still brings in hundreds of millions of dollars a year in revenue for 21st Century Fox. And veterans like Mr. Shine, with years of experience and deep relationships with network talent, provide continuity in the day-to-day operations during a time of upheaval.

Despite the scrutiny, Mr. Shine attended a gala reception in Manhattan this month, where he was surrounded by journalists and leading figures in television news. He declined to comment on his network or his position, saying only, “I’m here to have a good time.”

Correction: April 27, 2017

An earlier version of this article misstated the circumstances under which the Fox News co-president Bill Shine and the anchor Sean Hannity met in the 1990s on Long Island. They were working in talk radio, not local news.