US President Donald Trump has arrived at the Vatican for talks with one of his most high-profile critics, Pope Francis, after the two men exchanged sharp words during the presidential campaign last year.

Under clear blue skies, Trump received a tribute from the Swiss Guard in a Vatican courtyard where he was greeted by Archbishop Georg Ganswein, the prefect of the pontifical household.

Trump looked uncomfortable as he entered a small elevator taking him to the third floor of the Apostolic Palace, where he was accompanied by Ganswein and other officials along a frescoed corridor to the Pope's private study.

Following behind Trump were daughter Ivanka, her husband, Jared Kushner, a top White House aide, national security adviser HR McMaster and adviser Hope Hicks.

The Pope did not smile as he greeted Trump outside the study. Trump, seeming subdued, said "it is a great honour".

The two men then posed for photographs and the Pope kept a stern face while Trump beamed for the cameras. The meeting began at precisely 8.33am.

Trump's meeting with Pope Francis, 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 said last year 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.

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 8.30am on a Wednesday, an unusual day and an unusually early time.

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.