Mayor Eric Adams, who talks often about his faith, acknowledged on Saturday that he had felt some uncertainty — if not anxiety — about meeting Pope Francis.

But at the Vatican, as Mr. Adams stooped before the pope, he felt any disquiet he had wash away. Pope Francis placed his hand on the mayor’s right arm. Then, the two shook hands.

“I think that some people have a level of aura and energy and the ability to just calm people,” said Mr. Adams, who is Christian but not Catholic. “I think that’s what he possessed. In my prayers, I thank God for having the opportunity this morning.”

The meeting came on the second day of a three-day trip to Italy for Mr. Adams, who said he is trying to better understand the global conflicts that touch New York. The visit came as the mayor, who is up for re-election next year, faces difficulties in New York City, including lagging poll numbers and a federal investigation into his campaign fund-raising.

There was no specific agenda for the meeting between the mayor and the pope, which came as the pope met with participants of a conference about peace. But after the meeting, Mr. Adams said the two spoke about conflicts in Haiti, Africa and the Middle East. They talked about the Foundation to Combat Anti-Semitism, a nonprofit created by Robert Kraft, the owner of the N.F.L.’s New England Patriots.

“He responded affirmatively and said: ‘Eric, please pray for me as well,’” the mayor said.

Mr. Adams and the pope took part in the World Meeting on Human Fraternity, a conference organized by the Fratelli Tutti Foundation, which was founded by Pope Francis, that brought Nobel laureates and celebrities to Rome to promote peace.