Trump will later meet Italian President Sergio Mattarella and Prime Minister Paolo Gentiloni.
The meeting with the pope was the third stop on Mr Trump's nine-day foreign tour, and part of his world tour of religions after meeting leaders of Muslim nations in Saudi Arabia and visiting holy sites in Jerusalem.
The dessert is obviously very rich - could the pope have been poking fun at the president's stature? During the election the Pope on a visit to the Mexico-US border said that people who only think of building walls instead of bridges were not Christian.
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The picture of the two leaders may not be the only one to be remembered as iconic.
Melania and Ivanka Trump dressed in black and wore head veils to meet Pope Francis.
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According to the Economist, the Vatican described the meeting between the two as "cordial" and noted the Pope hopes to work with the Trump administration on "healthcare, education and assistance to immigrants".
The two exchanged gifts after the meeting.
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Shortly after her visit with Pope Francis, the first lady tweeted a photo, saying she was "humbled by the honor" to have visited with the pontiff. "Potica, ah yes", the Slovenian-born first lady smiled before stepping aside.
In return, Pope Francis gave Trump three of his writings, which he typically gives to heads of state, including "Amoris Laetitia", "Evangelii Gaudium", and "Laudato Si'" - his 2015 encyclical calling for climate change action.
As the meeting began in the Apostolic Palace, the Pope was unsmiling and subdued, staring at the floor as they stood for photographs, while Mr Trump beamed.
He later flew to Brussels where he was to meet Belgium's king and prime minister on Wednesday evening before a day of meetings with European Union and North Atlantic Treaty Organisation leaders on Thursday.
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