— President Obama joined Pope Francis on Thursday at the Vatican, a meeting of two world figures with radically different politics but a shared concern that the global economy is dangerously dividing rich and poor.

The visit, watched closely here by an avid media and curious Romans who leaned from balconies to see Obama’s motorcade pass, is the most symbolic stop of the president’s Europe trip.

The two greeted each other Thursday morning outside the Papal Library in the Small Throne Room, extending hands and smiles.

“Wonderful meeting you. I’m a great admirer,” Obama said. “Thank you, sir, thank you.”

The men withdrew into the Papal Library and took seats on opposite sides of the pope’s desk. “Thank you,” Obama said, “for receiving me.”

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The meeting lasted less than an hour. But the encounter has been charged with the politics of the world’s most powerful nation and one of its most influential religious movements, and by a pair of men who have sought to change the public character of the institutions they run.

Obama said that “the bulk of the time was spent discussing two central concerns” — the plight of “the poor, the marginalized and growing inequality” and the challenge of war in the world today. He said the talk underscored that although political leaders must find solutions, Francis has the power to focus public attention on the importance of resolving these issues.

“We spent a lot of time talking about the challenges of conflict and how elusive peace is around the world,” Obama said, particularly the Israeli-Palestinian negotiations, an issue of particular interest to the pope, who is scheduled to visit the Middle East in late May; the unrest in Syria and Lebanon; and the persecution of Christians.

“The theme that stitched our conversation together was a belief that, in politics and in life, the quality of empathy, the ability to stand in somebody else’s shoes and to care for someone even if they don’t look like you or talk like you or share your philosophy — that’s critical,” Obama said. “It’s the lack of empathy that plunges us into wars.”

Obama said he urged Francis to visit the United States, saying the country would receive him enthusiastically.

On U.S. domestic issues, the president acknowledged that Francis, born in Argentina, underscored the urgent need for immigration reform. Obama said the pope, as someone from Latin America, is particularly mindful of the plight of immigrants and the tragedy of family separations.

“I described to him how I thought there was an opportunity to make this right and get something passed” on immigration reform, Obama said.

In a statement, the Vatican called the meeting “cordial” and said that “views were exchanged on some current international themes, and it was hoped that, in areas of conflict, there would be respect for humanitarian and international law and a negotiated solution between the parties involved,” a possible reference to the crisis in Ukraine and the Middle East.

The statement also said that the leaders discussed “questions of particular relevance” to the Catholic Church in the United States, “such as the exercise of the rights to religious freedom, life and conscientious objection, as well as the issue of immigration reform.”

Obama, who although not Catholic has religious roots in the social gospel embraced by this first non-European pope, is pushing at home for a higher minimum wage, education spending to increase economic opportunity and changes in the tax code that would draw more money from the wealthy.

His political popularity, though, is wobbling. An AP-GfK poll this week showed that 59 percent of respondents disapprove of the way he is handling his job, a rating that is among the highest of his presidency.

“He is going mostly to bask in the glow of the new pope,” said Jeremy Shapiro, a visiting fellow at the Brookings Institution and a former adviser on Europe in the State Department earlier in Obama’s tenure.

“This isn’t really a foreign policy stop — so, in that sense, it’s very important to the president,” Shapiro said.

Obama came to office promising to change the world’s perception of the United States, emphasizing alliances over unilateral action, diplomacy over military measures and a “new beginning” with Islam after years of war in Afghanistan and Iraq.

“I do think that there is a potential convergence between what policymakers need to be thinking about and what he’s talking about,” Obama said at the news conference, referring to the pope. “He’s hopefully creating an environment in which those of us who care about this are able to talk about it more effectively. And we are in many ways following not just his lead but the teachings of Jesus Christ and other religions that care deeply about the least” among us.

The pope, too, has attempted in his first year to recast the image of the Catholic Church as an institution close to its adherents. He has struck a more tolerant tone on homosexuality, condemned the lavish lifestyles of some church figures, and personally ministered to the poor, the imprisoned and others on society’s growing margins.

Obama has praised such commitment.

But Francis has significant political disagreements with the president, including on immigration, contraception requirements in the Affordable Care Act and gay marriage.

Obama presented the pope with what the White House described as “a custom-made seed chest featuring a variety of fruit and vegetable seeds used in the White House Garden.” The gift echoed the pope’s announcement this month that he would open the gardens of the papal summer residence, the Apostolic Palace of Castel Gandolfo, to the public.

The White House said the chest is made from “American leather, and features reclaimed wood from the Basilica of the National Shrine of the Assumption of the Blessed Virgin Mary, which is one of the oldest Catholic cathedrals built in the United States.” It said seeds will also be donated, “to yield several tons of produce, to a charity of the pope’s choosing.”

Obama received a copy of Francis’s exhortation, the Joy of the Gospel, an extended essay in which he calls for a church that “is poor and for the poor.”

Obama said he is likely to read it “when I’m deeply frustrated. I’m sure it will give me strength and calm me down.”