Under clear blue skies, Mr Trump received a tribute from the Swiss Guard in a Vatican courtyard when he arrived. "We can use peace", the President said, concurring with the symbolism. But after a half-hour meeting behind closed doors, Francis seemed to have cheered up considerably. "Potica?" - a reference to a calorie-laden cake from Slovenia, her country of birth.
The two men have in the past clashed on issues such as migration, climate change and a Mexico-US wall.
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".
Trump, the 13th president to visit the Vatican, also toured the Sistine Chapel.
The report, citing unnamed sources, did not provide further details on the alleged deliberations. At the end of the meeting, Trump told the Pontiff: "I won't forget what you said". The president and pope have a contentious history, but appeared on good terms after their conversation.
Pope Francis smiled faintly as he greeted Mr Trump outside the study and was not as outgoing as he sometimes is with visiting heads of state.
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Orrin Hatch was one of the few senators who would admit that the CBO score caused "a lot of concern" among Republicans. Senate Republicans have been holding closed-door meetings to try writing their own health care overhaul.
"Well, I'll be reading them", Trump said after the gift exchange.
Writings on family, the Christian Gospel, and the recent World Day of Peace message - personally signed - were among the Pope's other gifts to Trump, who gave the religious leader books by Martin Luther King, Jr.
Trump took to Twitter after meeting the pope saying: "Honor of a lifetime to meet His Holiness Pope Francis".
However, the first lady's spokeswoman, Stephanie Grisham, today confirmed to CNN that Trump is indeed Catholic. 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.
Protests are also expected on 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.