As with Fox’s ubiquitous promotion of its slogan, conservatives’ appropriation of the “fake news” label is an effort to further erode the mainstream media’s claim to be a reliable and accurate source.

“What I think is so unsettling about the fake news cries now is that their audience has already sort of bought into this idea that journalism has no credibility or legitimacy,” said Angelo Carusone, the president of Media Matters, a liberal group that polices the news media for bias. “Therefore, by applying that term to credible outlets, it becomes much more believable.”

Conservative news media are now awash in the “fake news” condemnations. When coverage of Mr. Trump’s choice for labor secretary, Andrew F. Puzder, highlighted his opposition to minimum wage increases, the writer and radio host Erick Erickson wrote that Mr. Puzder should have been getting more credit for pointing out that such increases lead to higher unemployment. “To say otherwise is to push fake news,” he wrote. (The effects actually have been found to vary from city to city.)

Infowars, the website run by the conservative provocateur and conspiracy theorist Alex Jones, labeled as “fake news” a CNN report that Ivanka Trump would move into the office in the White House normally reserved for the first lady.

Mr. Trump has used the term to deny news reports, as he did on Twitter recently after various outlets said he would stay on as the executive producer of “The New Celebrity Apprentice” after taking office in January. “Ridiculous & untrue — FAKE NEWS!” he wrote. (He will be credited as executive producer, a spokesman for the show’s creator, Mark Burnett, has said. But it is unclear what work, if any, he will do on the show.)

Many conservatives are pushing back at the outrage over fake news because they believe that liberals, unwilling to accept Mr. Trump’s victory, are attributing his triumph to nefarious external factors.

“The left refuses to admit that the fundamental problem isn’t the Russians or Jim Comey or ‘fake news’ or the Electoral College,” said Laura Ingraham, the author and radio host. “‘Fake news’ is just another fake excuse for their failed agenda.”