"Thank you, thank you", Trump told Francis as they shook hands after the meeting.
Mr Trump also told the pope he was committing more than US$300 million (Dh1.1 billion) to help prevent or tackle starvation in Yemen and several countries in Africa.
Camilla, Duchess of Cornwall, wore cream and did not cover her head when meeting Francis last month, although she had worn black and a veil at a 2009 meeting with Pope Benedict XVI.
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"I give it to you so you can be an instrument of peace", he said in Spanish.
Trump said that the most important issue during his time in Belgium was terrorism after the "horrible situation" in Manchester, England, where a suicide bomber killed 22 people in an attack claimed by the Islamic State. "Thank you. I won't forget what you said". But there are few other areas where their views align. She repeated "potizza", which is a Slovenian baked treat. Francis welcomed Trump to the Apostolic Palace, where he goes only for official occasions, as the pontiff resides in the Vatican guesthouse rather than the Papal Apartments.In February 2016, shortly after celebrating a Mass in Mexico just yards from the border, Pope Francis was asked by reporters about then-candidate Trump's promise to build a wall the entire length of the border.A Vatican statement is expected shortly.
After Trump's private meeting with the Pope, Melania and others were invited to join the pair in the papal library.
More potentially awkward meetings await the President on the next leg of his trip to Belgium where he is attending a North Atlantic Treaty Organisation summit, meeting the leaders of the European Union as well as the King, Queen and Prime Minister of Belgium. Details of the traditional gifts exchanged by Trump and Francis have not yet been revealed, the report said.
The two talked privately for about 30 minutes through translators.
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Mr Trump, who BBC Europe editor Katya Adler said seemed star-struck, said of the Pope: "He is something, he's really good". Climate change activists projected the words "Planet Earth First" on the massive dome of St. Peter's Basilica at the Vatican Tuesday night and protests are expected Wednesday in Rome and later in the week when Trump travels to Brussels for a North Atlantic Treaty Organisation meeting and Sicily for a G7 gathering.
Ivanka Trump met Wednesday with a group of African women in Rome who were trafficked into prostitution rings, a private encounter said to have moved her to tears.
The president is midway through a grueling nine-day, maiden global journey which has included Middle East stops in the cradles of Islam and Judaism. But the timing Wednesday was tight as Francis had his weekly general audience. And in Israel, Trump reaffirmed his commitment to strong ties with the nation's longtime ally and urged both the Israelis and the Palestinians to begin the process of reaching a peace deal.
Trump retorted that it was "disgraceful" for the pope to doubt his faith. Climate change activists projected the words "Planet Earth First" on the massive dome of St. Peter's Basilica at the Vatican Tuesday night and protests are expected after Trump arrives in Brussels for a North Atlantic Treaty Organisation meeting and Sicily for a G-7 gathering.
At the Vatican, while Mrs Trump strictly followed tradition and protocol by wearing black and a mantilla, other high-profile visitors have taken liberties with their attire.
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And it leaves open a slew of questions that Trump may be pressed to address while he is in Israel and in the West Bank. The church was built to commemorate the location where most Christians believe Jesus was crucified and buried.
A source close to the White House told CNN that Spicer not being brought along to the meeting was "a slight", and that to meet Papa Francesco was "all he wanted".