VATICAN CITY — Pope Francis put climate change on the agenda of his first meeting with President Trump on Wednesday, and the subject is likely to come up again and again in the president’s encounters with other world leaders in the coming days.

That could put Mr. Trump on the back foot after what had been an energetic swing through the Middle East.

The pope presented the president with a copy of his influential encyclical on preserving the environment, while in a broader meeting, Cardinal Pietro Parolin, the Vatican’s secretary of state, urged Mr. Trump not to pull the United States out of the Paris climate accord.

Mr. Trump told his Vatican hosts that he would not make a final decision until after he returned to the United States, despite some expectations that he could announce a decision at the Group of 7 summit meeting in Italy this weekend.

The leaders of Germany, France and Canada have all pressed Mr. Trump on the Paris accord, and they are likely to renew their pleas at the summit meeting, in the Sicilian town of Taormina. Their argument, officials said, will be that withdrawing from the accord would damage America’s credibility and hurt Mr. Trump’s ability to achieve other parts of his agenda.

“They were encouraging continued participation,” Secretary of State Rex W. Tillerson told reporters about the message from the Vatican. “We had a good exchange on the difficulty of balancing addressing climate change, and ensuring that you still have a thriving economy and you can still offer people jobs so they can feed their families.”

In their first encounter, the pope and the president, two men with starkly different worldviews, sought to bridge the chasm between them with a handshake, a private audience and a mutual pledge to work for peace.

They stuck mainly to protocol, avoiding a public reprise of the barbs they aimed at each other during Mr. Trump’s presidential campaign or the pope’s thinly veiled critiques of the new president as a symbol of a dangerously reinvigorated nationalism.

But there was also a sense in the Vatican that Mr. Trump was easier to talk to than his tough language on the campaign trail or his sharp words toward Francis had led them to believe. That could be particularly true on the issue of American participation in the Paris accord, where there are sharply conflicting views inside the West Wing.