"And so it is what is, I guess, but it's very unfortunate," said Milwaukee Archbishop Jeffrey S. Grob. "It's a very serious time."

The president suggested Catholics, who have criticized the apparently A.I.-generated image, were not offended, and said that anyone who was “can’t take a joke.”

President Donald Trump on Monday dismissed the backlash against an AI-generated image of him as the pope posted by the White House on social media, saying it was a harmless joke, but communications experts said they did not see the funny side.