"By putting everybody together you can really build a coalition and show that it's not a Muslim problem, it's not a Jewish problem, it's not a Catholic problem, it's not a Christian problem, it really is a world problem", the official said. Referring to a Slovenian cake.
The Pope had said that a person who thinks only about building walls, wherever they may be, and not building bridges, was not a Christian.
He continued things on by giving the President the holy silent treatment.
Before the spat, Trump had mostly praised Francis, congratulating Catholics on the choice of the new pope in 2013 and saying via Twitter, "People that know him love him!" The meeting appeared quite respectful but the Pope left Trump with an epic gift: the encyclical he penned on climate change. That acceptance was seen as an effort by the pope to relax some rules of the Vatican.
The American delegation also included national security adviser H.R. McMaster, Secretary of State Rex Tillerson and two other State Department officials, Margaret Peterlin and Brian Hook.
Trump next heads to Brussels for meetings with North Atlantic Treaty Organisation leaders. When he changed his mind, the Vatican squeezed him in at 8:30 a.m. on a Wednesday morning, an unusual day and an unusually early time. "He is something", Trump later said of his host.
Trump responded: "We can use peace".
While in Italy, Trump also met with Italian President Sergio Mattarella and Prime Minister Paolo Gentiloni.
Mr Trump's Vatican visit was the third leg of his overseas trip, after stops in Saudi Arabia, Israel and the Palestinian territories.
As he bade the pope farewell, Trump told him, "I won't forget what you said".
Pope Francis urged Trump to be a peacemaker in what was expected to be a tense meeting after the two had exchanged sharp words a year ago.
Donald, Melania, Ivanka and her husband Jared Kushner visited the Vatican as the President arrived for one of his most high-profile talks on his first foreign tour.