President Trump meets Pope Francis

US President Donald Trump met Pope Francis at the Vatican on Wednesday in the first face-to-face encounter between the two world leaders, who have clashed on several issues.

The pope greeted Trump outside his study where they shook hands. Trump said, "It is a great honour."

At the end of the private encounter, the pope gave the president a small sculptured olive tree symbolising peace. Trump thanked him and said, "We can use peace."

The pope also gave Trump a signed copy of the message he delivered at the last World Peace Day and three of his major writings, including his 2015 encyclical on the need to protect the environment.

"Well, I'll be reading them," Trump said.

He gave the pope a boxed set of writings by US civil rights icon Martin Luther King.

As Trump left he told his host, "Thank you, I won't forget what you said."

The audience with the leader of the world's 1.2 billion Catholics came on the third leg of Trump's first overseas trip as president. He has already visited Saudi Arabia, Israel and the Palestinian territories.

Trump is also meeting Italy's president and prime minister before setting off to Brussels for a NATO meeting on Thursday.

Sharp exchange ahead of Trump's election

Trump and the Roman Catholic pontiff made headlines last year – after the two men exchanged sharp words during the presidential campaign – over their differing views on issues that include migration and climate change.

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 to question his faith.

"If and when the Vatican is attacked by ISIS [Daesh], 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.

A fresh start?

Pope Francis was in a conciliatory mood ahead of his meeting with the US president, saying he would be "sincere" with Trump and did not want to judge him before listening to him in person.

Trump was heading to the Vatican with a message of peace in the Middle East.

Part of Trump's motivation for meeting the pope was to dramatise how the three major religions should rally against the threat from terror.

"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.

In Saudi Arabia, Trump urged Arab and Islamic leaders to unite and do their share to defeat extremism and "drive out" terrorists, while singling out predominantly-Shia Iran as a key source of funding and support for militant groups.

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

Pope Francis holds his weekly audience with the general public on Wednesday at 10:00am in St Peter's Square.