But Francis has apparently grown frustrated in recent months with the hostile corners of the American church and their media megaphone. The American Catholic television network, EWTN, is arguably the world’s largest, and its biggest star, Raymond Arroyo, a favorite of Mr. Trump, has frequently hosted guests hostile to Francis and Mr. Biden.

EWTN owns an array of English-language Catholic outlets that are popular with American bishops and many American churchgoers, and which have featured Carlo Maria Viganò, the rogue archbishop and former papal envoy to the United States who has called for the pope’s resignation.

In September, an EWTN correspondent covering the White House drew a sharp response from Mr. Biden’s press secretary, Jen Psaki, when he asked her, “Why does the president support abortion when his own Catholic faith teaches abortion is morally wrong?”

“He believes that it’s up to a woman to make those decisions with her doctor,” Ms. Psaki replied. “I know you’ve never faced those choices. Nor have you ever been pregnant, but for women out there who have faced those choices, this is an incredibly difficult thing.”

In March, Francis told the EWTN reporter and cameraman onboard a papal flight to Iraq that the network “should stop bad-mouthing me,” according to a report in the Jesuit magazine America. The reporter on the flight declined to comment. The network’s Rome bureau chief did not return a request for comment.

And on his recent trip to Slovakia, Francis also joked in a meeting with Jesuits who asked about his health that he was “still alive, even though some people wanted me to die.” He also pointed out “a large Catholic television channel that has no hesitation in continually speaking ill of the pope.”

“They are the work of the devil,” the pope added. “I have also said this to some of them.”

Leaders among the conservative American bishops rallied to the network’s defense. Archbishop Charles J. Chaput, who led the archdiocese of Philadelphia and who is a former EWTN board member, wrote last week that “any suggestion that EWTN is unfaithful to the Church” is “simply vindictive and false.”

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