JUDY WOODRUFF: President Trump's first trip abroad placed him at the Vatican today, marking Mr. Trump's first meeting with the leader of the Catholic Church.
Special correspondent Malcolm Brabant is in Rome for us tonight, and he has this report.
MALCOLM BRABANT: It was a meeting of two men with a difficult history.
After a public greeting, President Trump and Pope Francis spoke privately for half-an-hour. Later, there were introductions all around, and group pictures, with Mr. Trump smiling broadly, and the pontiff stone-faced.
Just a little over a year ago, they clashed publicly. The pope took on the Trump campaign pledge to build a wall along the U.S.-Mexico border.
POPE FRANCIS, Leader of Catholic Church (through interpreter): A person who thinks only about building walls, wherever they may be, and not building bridges, is not a Christian.
MALCOLM BRABANT: The candidate answered with a dig of his own.
PRESIDENT DONALD TRUMP: For a religious leader to question a person's faith is disgraceful.
MALCOLM BRABANT: Today, instead of barbs, they exchanged gifts. Mr. Trump presented the pope with a first-edition set of Martin Luther King Jr.'s works. Francis offered his three main teaching documents and an olive branch medal.
PRESIDENT DONALD TRUMP: We can use peace.
MALCOLM BRABANT: Later, after touring the Sistine Chapel and St. Peter's Basilica, and the president offered a new assessment of the pope.
PRESIDENT DONALD TRUMP: He is something. He is really good. We had a fantastic meeting. We had a fantastic tour. It was really beautiful.
MALCOLM BRABANT: President Trump's take on his meeting with Pope Francis differs greatly from the interpretation of veteran Vatican analysts. They believe that the president was exaggerating. The Vatican issued an unusually brief statement about the discussions.
RICCARDO CRISTIANO, Reset Magazine: They qualified the meeting as cordial, which means that the meeting wasn't a cold one, but a cordial one, but, in any case, it was not a warm meeting.
MALCOLM BRABANT: Longtime Vatican watcher Riccardo Cristiano says he doubts there was any meeting of minds.
RICCARDO CRISTIANO: I think that it was a opportunity to meet, but also the impression is that they understood they have different perspectives.
MALCOLM BRABANT: Analyst Robert Mickens was far more upbeat. He says it was a success for the Vatican.
ROBERT MICKENS, La Croix International: Pope Francis is always very gracious. He likes to build bridges of encounter. It's very, very important to get the superpower online with the soft power, the Holy See.
MALCOLM BRABANT: The president also met with the Vatican's secretary of state, who encouraged continued U.S. participation in the Paris climate agreement.
Secretary of State Rex Tillerson gave his own appraisal on the flight from Rome to Brussels.
REX TILLERSON, U.S. Secretary of State: Well, we had a good exchange on the difficulty of balancing, addressing climate change, responses to climate change, and ensuring that you still have a thriving economy.
MALCOLM BRABANT: The president arrived in Brussels this evening for meetings with European Union and NATO officials, and was greeted by the Belgian prime minister and royal family.
Thousands of demonstrators also turned out, protesting the president's immigration and environmental policies.
For the PBS NewsHour, I'm Malcolm Brabant in Rome.