President Trump said on Monday that he “had nothing to do with” a depiction of himself as the pope that was shared on his and White House social media accounts over the weekend, distancing himself from the apparently A.I.-generated image that has agitated Catholics.

“I had nothing to do with it,” Mr. Trump said while taking questions in the Oval Office. “Somebody made up a picture of me dressed like the pope, and they put it out on the internet. That’s not me that did it, I have no idea where it came from — maybe it was A.I. But I have no idea where it came from.”

Mr. Trump, responding to a question about Catholics who are displeased with the image of him dressed in white papal robes and a ceremonial headdress, also attempted to downplay the mounting criticism.

“They can’t take a joke,” Mr. Trump said, quickly telling the reporter, “You don’t mean the Catholics; you mean the fake news media. The Catholics loved it.”

But Catholics across the country, including a prominent American cardinal, have suggested the image is offensive, especially as they mourn the death of Pope Francis. Cardinal Timothy M. Dolan of New York, in Rome for the papal conclave, said when asked about the image on Sunday that he hoped it was not the president’s doing.

“I hope he didn’t have anything to do with that,” Cardinal Dolan said. Asked if he was offended by it, the cardinal demurred but called the image a “brutta figura,” meaning it had made a bad impression.