But Francis seemed eager to address one pressing geopolitical issue. He urged the United States and North Korea to step away from the brink and avoid a nuclear conflict that could, he said, be disastrous for “the future of humanity.”

His comments came just days after Mr. Trump said in an interview with Reuters that there was a chance “that we could end up having a major, major conflict with North Korea.” The president’s remarks seemed to undercut remarks by others in his administration to ease the dispute by raising the possibility of direct negotiations between the United States and North Korea.

Mr. Trump is scheduled to make his first trip abroad as president in May. His exact itinerary is unclear, but he is expected in Taormina, Sicily, for a meeting of the world’s leading economic powers at the end of the month. A visit with the pope is standard for American presidents traveling to Italy, but the two world leaders have a rocky history.

In February 2016, Francis responded to a question about Mr. Trump by saying, “A person who thinks only about building walls, wherever they may be, and not building bridges, is not a Christian.”

The pope’s view does not seem to have changed. In one of his Cairo speeches, Francis said: “Demagogic forms of populism are on the rise. These certainly do not help to consolidate peace and stability.”

All of that has led to doubts about whether a meeting will actually happen. During a news conference at the White House this month with Prime Minister Paolo Gentiloni of Italy, Mr. Trump said, “I look very much forward to meeting the pope.” Immediately after, Mr. Trump’s spokesman, Sean Spicer, acknowledged that no meeting had been scheduled.

That was still the case as of Saturday evening.

“I still haven’t been informed by the secretary of state that a request has been made,” the pope said, “but I meet every head of state who asks for an audience.”