Trump has threatened to pull out of the Paris climate accord and cancel payments to the United Nation's climate change programs, while the pope wrote a 181-page encyclical on protecting the earth, "Laudato Si" (Praise Be).
Pope Francis also gave Trump this year's "message of peace" with a personalized inscription he had written. Afterwards, the Trumps were given a private tour of the Sistine Chapel and St Peter's Basilica.
"It is my desire that you become an olive tree to construct peace", the Pope said, speaking in Spanish.
The president responded, "We can use peace".
Trump fired back, saying: "For a religious leader to question a person's faith is disgraceful".
A Vatican statement said the meeting was "cordial" and that the Vatican hoped there could be "serene collaboration" between the USA government and the American Catholic Church, including "assistance to immigrants".
The president and the pope have something of a complicated past.
President Trump kindly accepted his thoughtful gift.
The audience took place in the private library of the Apostolic Palace, the official papal residence that Francis does not use, having opted instead for modest lodgings in a Vatican guesthouse. Over the weekend, he stopped in Saudi Arabia, where he delivered an address to Muslim leaders, and Monday through Tuesday he visited Israel and the West Bank and met with Israeli and Palestinian leaders.
After visits with the Muslims and Jews, President Donald Trump took on perhaps his toughest audience yet: the Catholics. Smiling broadly, Trump was heard to say "thank you so much", before commenting, "it is such an honour to be here".
And even the pontiff's congratulatory message sent to mark Trump's inauguration contained a sly reference to their disagreement, as the pope wrote that he hoped the United States' global stature would "continue to be measured above all by its concern for the poor, the outcast and those in need". The president signed a $110 billion arms deal with Saudi Arabia, opened a center for "combatting extremism" in the Middle East and met with several world and interfaith leaders from each of the major religions-Islam, Judaism and Christianity.
The White House said Trump and the pontiff "focused on how the United States, the Holy See, and the worldwide community can work together to combat terrorism" in their closed-door meeting. Team Trump was due in Brussels on Wednesday afternoon for meetings with European Union and North Atlantic Treaty Organisation officials before returning to Italy for the G7 summit in Sicily on Friday and Saturday. "I hold out hope that the Holy Father can help President Trump soften some of his views and that Trump can help Francis understand his priorities", Rossi said. There were 12 people in his entourage, including First Lady Melania Trump; daughter Ivanka, Tump's assistant and his son-in-law Jared Kushner, his assistant and senior advisor. "I hope you do", Trump said.
The First Lady had the Pope bless a religious object, probably a rosary.
Francis and Trump have clashed on some issues in the past, such as the president's vow during the 2016 election campaign to build a massive wall at the Mexican border in order to keep illegal immigrants and traffickers out of the country.