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Trump arrived for a short private audience at the Apostolic Palace along with his wife Melania, daughter Ivanka and son-in-law Jared Kushner.
The US President was greeted warmly by Francis before they sat down for the private meeting at which only a translator was present.
Trump could be heard saying it was "an honour" to be there during the meeting. At one point, the Pope jokingly asked Melania, "what she fed her husband", the Guardian reported.
The seemingly genial meeting offered no hint of the rocky start to the pair's relationship last year, when the Argentinian pontiff questioned then-candidate Trump's Christian credentials, the report said.
US Secretary of State Rex W Tillerson and National Security Adviser H R McMaster were among Trump's delegation to the Vatican.
After Trump's private meeting with the Pope, Melania and others were invited to join the pair in the papal library.
Melania and Ivanka wore black dresses and veils, traditional Vatican attire for women, considered respectful, though not mandatory.
After arrival, Trump was greeted by Georg Gänswein, a German archbishop and prefect of the papal household. Details of the traditional gifts exchanged by Trump and Francis have not yet been revealed, the report said.
For Trump, who landed in Rome after stops in Saudi Arabia and Israel, the audience in the Vatican caps a tour of the ancestral homes of three of the world's great monotheistic religions.
Trump and the Pope have diametrically opposite views on issues as varied as immigration, climate change and arms sales.
Trump will later meet Italian President Sergio Mattarella and Prime Minister Paolo Gentiloni. He will then fly to Brussels for a NATO summit.
Later, Ivanka is expected to visit Sant'Egidio, a Rome charity centre devoted to migrants. Melania will visit the Bambino Gesu children's hospital.
At an earlier news conference, the Pope said he wouldn't judge Trump before their meeting or seek to convert him on political issues. Instead, he'd look for areas of agreement.
The US President vowed to help Israelis and Palestinians achieve peace, as he ended the Middle East leg of his tour on Tuesday.
Trump had begun his foreign trip with a two-day stop in Saudi Arabia over the weekend, urging Muslim countries to take the lead in combating radicalisation. He will fly to Brussels later in the day for a NATO summit, and will wrap up his tour on Friday after the G7 summit on the Italian island of Sicily.