After concluding the visit to Rome, Trump will leave for Brussels, where he will attend a North Atlantic Treaty Organisation meeting before returning to Italy to participate in the G-7 summit on May 26th and 27th in the Sicilian town of Taormina.
Air Force One landed at Leonardo da Vinci airport, where Trump and his wife Melania were greeted by Italian Foreign Minister Angelino Alfano.
Trump reacted to the pontiff's comments by calling Francis "disgraceful" for doubting his faith. After the cameras left the two began the private portion of their conversation, which lasted about 30 minutes.
While President Trump flashed a wide grin, the Pope offered only a modest smile - his demeanor, business-like. Mark Miles were present.
The two men had never met before Wednesday morning but they have significant history having clashed publicly over subjects ranging from migration to unbridled capitalism and climate change.
In addition to being a 9-day, 5-country tour of world religions during which the president has been trying to sell a message of unity, it's also been a tour of religious protocols and devotional clothing conventions for first lady Melania Trump and first daughter Ivanka Trump, and an exercise in the politics of religious head coverings.
The gesture has political undertones, as the Pope urged action to be taken to combat climate change effects in the encyclical, while Trump has stated climate change is a hoax.
The environmental campaign group's Executive Director Jennifer Morgan said: "We delivered to Trump a message that his first priority must be to people and planet, not the profits of polluters".
Knowing that Pope Francis frequently has quoted the Rev. Martin Luther King Jr., Trump presented Pope Francis will a large gift box containing five of the slain civil rights leader's books, including a signed copy of The Strength to Love. Members of the delegation each received a medal and a rosary from the pontiff.
Meanwhile, the first lady went to the Vatican-owned Bambino Gesu children's hospital - right next door to the Pontifical North American College, which is where USA seminarians in Rome live.
As Trump and the pope said goodbye at the door of the study, Trump told the pope: "Thank you, thank you". But the timing Wednesday was tight as Francis had his weekly Wednesday general audience.
Reporters in the room thought initially that the First Lady had replied "Pizza!" Bambino Gesu sits next to the Pontifical North American College on top of Rome's Gianicolo hill, and is among the most important pediatric hospitals in the world. The Sant'Egidio Community is often praised by Pope Francis for their work with the poor and refugees, in particular.
The president, however, dodged a question on whether or not they also talked about issues to do with global warming, which has increasing become a subject of concern in the recent past. He appreciated President Barack Obama's 2014 gift of seeds from the White House garden that were later planted at the summer papal retreat at Castelgandolfo.