The pope influenced the political debate in the United States and beyond with his outspoken denunciation of global inequality and his critique of global capitalism. During his visit to the Vatican in March, Mr. Obama lavished praise on the pope as he sought to align his own political agenda on issues such as raising the minimum wage with that of Francis, whose global popularity, for the moment, seems to transcend religion.

“If you look around the world, there are very few political leaders who are relatively untainted,” said Philip Jenkins, a history professor who teaches at the Institute for Studies of Religion at Baylor University. “People want to believe there is somebody good and charismatic, and a good authority figure, out there.”

But plunging into Middle East politics can be especially perilous. In a region where religious divisions overlay the political impasse, Francis’ prayer summit “is taking the negotiations to another level — a meeting before God,” said the Rev. Jamal Khadar, head of a West Bank seminary and a spokesman for the pope’s visit. The idea, he added, is to “make religion part of trying to find a solution instead of it being seen as a negative and a complication.”

Oded Ben Hur, a former Israeli ambassador to the Holy See, said by making a personal invitation for a prayer summit meeting, Francis eschewed Vatican protocol and tradition while showing atypical boldness. Most pontiffs, he said, “don’t rock the boat.”

“This is different,” he added. “It’s a balance, but the fact is, there is a move somewhere. He’s not conventional in that sense. When he thinks something, he expresses it.”

Sunday was the second of Francis’ three-day sojourn through the Holy Land, a trip with a carefully designed itinerary. In a delicate diplomatic dance, the pope helicoptered from Bethlehem to Tel Aviv for an official head-of-state welcome to Israel, then back to Jerusalem for an ecumenical dinner with the Orthodox Patriarch of Constantinople.