President Trump on Tuesday had a ready answer when reporters asked who he would like to see become the next supreme pontiff. “I’d like to be pope,” he joked to reporters at the White House. “That would be my number one choice.”

He took the joke a step further on Saturday, sharing on social media what appeared to be an A.I.-generated photo of himself wearing the traditional vestments of the pope. The photo depicts him in a white cassock with a cross around his neck, his face solemn as he raises a pointed finger.

The origins of the photo were not immediately clear, and Mr. Trump did not include any commentary in his post. He shared the image on Truth Social, Instagram and X, and the White House reposted it on its official Instagram and X accounts.

The idea of “Pope Trump,” as some people called it, was immediately polarizing. Some religious people, including Catholics, did not see the humor in it, calling the photo offensive, at a time when millions of people were still mourning Pope Francis, who died on Easter Monday. Several commenters on Truth Social, which is run by a company controlled by Mr. Trump, called the post sacrilegious and said it fueled misinformation.

Michael Steele, a former chair of the Republican National Committee, said posting the photo during a period of mourning was evidence that Mr. Trump was “unserious and incapable.”

Dennis Poust, executive director of the New York State Catholic Conference, the public policy arm for the state’s Catholic bishops, said the post was shocking and “disrespectful,” and came at a particularly raw moment.

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