"We can use peace", the president replied.
In addition to the customary gift of these three documents, Francis also gave President Trump a copy of his message for the 2017 World Day of Peace, saying: "I signed it personally for you".
Trump has expressed skepticism about global warming and possible causes, and he has promised changes to spur more coal and oil production in the U.S.
Since first appearing in the political spotlight beside her husband, business tycoon-turned-45th US president Donald Trump, the Slovenian-born woman has been labeled everything from a gold-digging hooker to an illiterate foreigner (she's actually fluent in five languages, but whatever, Chelsea Handler). "And I hope they reached some sort of meeting of the minds on several issues".
Trump has been a sharp critic of North Atlantic Treaty Organisation countries that don't spend the agreed-upon 2 percent of their gross domestic product on defense, and Secretary of State Rex Tillerson said the president indeed planned to push allies hard on that issue. Those are non-negotiable issues of paramount importance. Do you think they need to tone it down?
Melania asked if the Pope would bless her rosary. "I think you will enjoy them", Trump told Francis, as he presented him with a first-edition set of King's writings, recalling the Pope's address to Congress in 2015 in which he quoted King. It went on to say it hoped there could be "serene collaboration" between the US government and the American Catholic Church, including, it said pointedly, "assistance to immigrants".
Because of the pope's weekly general audience, Pope Francis and Trump met at 8:30 a.m., an unusually early hour for a formal papal meeting.
Accompanied by the archbishop up an elevator and down a frescoed hallway, the president passed more Swiss Guards in the Clementine Hall.
Francis and Trump's past spats include the pope describing plans for a border wall with Mexico as not Christian and Trump evoking a possible Islamist attack on the Vatican which would make the pontiff glad to have him as president.
With their meeting on the horizon, Francis has said he always tries to find "doors that are at least a little bit open".
Outside the Quirinale Palace, the Italian president's official residence, where a small crowd mostly of tourists gathered to catch a glimpse of Trump in the distance down a closed avenue, 50-year-old Ragna, a Danish banker, said she did not really know why she was waiting. "We had a fantastic meeting", the president said.
After the meeting, First Lady Melania paid a visit to the Vatican-owned Pediatric hospital Bambino Gesu, also known as the "Pope's hospital".
Later in the morning, Trump, 70, was to call on Italy's president and prime minister while Melania visits a children's hospital and Ivanka discusses migration and people trafficking with members of the St Egidio religious community.