CNN's Chris Cillizza said, "The Vatican put out a nice statement after their meeting saying the two leaders talked about 'the promotion of peace in the world through political negotiation and [inter-religious] dialogue".
Asked how Trump responded to Cardinal Parolin's encouragement to stick with the Paris climate agreement, Tillerson said: "The president indicated we're still thinking about that, that he hasn't made a final decision".
A Vatican statement said the meeting was "cordial" and that the Vatican hoped there could be "serene collaboration" between the U.S. government and the American Catholic Church, including "assistance to immigrants".
President Trump is meeting with the prime minister before talks this week with North Atlantic Treaty Organisation and European Union officials.
The early arrivals at the Brussels North Station were shouting: "We don't want Trump!" On the campaign trail, after the Pope told journalists that building walls is not a Christian act, Trump questioned whether he was a pawn of the Mexican government and called him "disgraceful" for questioning his religion.
"We can use peace", said Trump.
He later flew to Brussels where he was to meet Belgium's king and prime minister on Wednesday evening before a day of meetings with European Union and North Atlantic Treaty Organisation leaders on Thursday.
Francis gave Donald Trump a large medal by a Roman artist, inscribed with an olive branch, a symbol of peace.
Other gifts given to the pope included a set of first-edition books by Dr. Martin Luther King Jr. and piece of granite from the King "Stone of Hope" monument in Washington, D.C. "I won't forget what you said".
As Mr Trump and the pope said goodbye at the door of the study, Mr Trump told him: "Thank you, thank you".
It also opposes his plan to build a wall on the US border with Mexico.
"A person who thinks only about building walls, wherever they may be, and not building bridges, is not Christian", Francis said then.
President Donald Trump is meeting with Belgian Prime Minister Charles Michel in Brussels.
In Saudi Arabia on Sunday, Trump implored Middle Eastern leaders to extinguish Islamic extremism from the region and described it as a "battle between good and evil" rather than a clash between the West and Islam.
While Trump received warm welcomes in Riyadh and Jerusalem, the reception could grow cooler now that he's reached Europe, site of widespread protests after his election. He spent the night at the USA ambassador to Italy's residence and will make the drive to the Vatican early Wednesday morning.