Trump's meeting at the Vatican's Apostolic Palace, his third stop on a nine-day foreign tour due to end on Saturday, is part of his world tour of religions after meeting leaders of Muslim nations in Saudi Arabia and visiting holy sites in Jerusalem.
But while his talks in Saudi Arabia and Israel were mostly friendly, the meeting between the head of the Roman Catholic Church and the thrice-married, blunt-spoken Trump could be a little more confrontational.
The pope last year said a man who thinks about building walls and not bridges is "not Christian," a sharp reprimand for Trump's vow to build a wall along the US border with Mexico.
Trump said it was "disgraceful" of the Argentine-born pope, who represents just over half of the world's two billion Christians, to question his faith.
"If and when the Vatican is attacked by ISIS, which as everyone knows is ISIS' ultimate trophy, I can promise you that the pope would have only wished and prayed that Donald Trump would have been president," Trump said during the campaign.
Trump's softer stance on environmental regulations also is at odds with Francis' view that climate change is caused mostly by human activity.
The Vatican also took a dim view of Trump's anti-Muslim campaign rhetoric, although Trump softened his tone considerably in a major speech in Riyadh.
Francis said last week he would be "sincere" with Trump but did not want to judge him before listening to him in person.
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Part of Trump's motivation for meeting the pope was to dramatise how the three major religions should rally against the threat from Islamist militants.
“We thought that this trip was essential to put together the Muslim faith, the Jewish faith and then the Catholic faith, the Christian faith," said a senior White House official who briefed reporters on Trump's Air Force One flight to Rome.
"By putting everybody together you can really build a coalition and show that it’s not a Muslim problem, it’s not a Jewish problem, it’s not a Catholic problem, it’s not a Christian problem, it really is a world problem," the official said.
Trump at first did not plan to stop in Rome during his visit to Europe, which some in the Vatican saw as a snub. When he changed his mind, the Vatican squeezed him in at 8:30 a.m. on a Wednesday morning, an unusual day and an unusually early time.
Francis holds his weekly audience with the general public on Wednesday at 10 a.m. in St Peter's Square.
After the meeting, Trump moves on to Brussels for a NATO summit, followed by the last stop on his trip, to a Group of Seven summit in Sicily.
