VATICAN CITY — President Obama and the Vatican gave distinctly different accounts of the president’s audience with Pope Francis on Thursday, with Obama stressing their common ground on poverty and inequality but Vatican officials emphasizing concerns over Obama’s health care law, which mandates contraception coverage.

Obama described himself as “incredibly moved” by his nearly hourlong session with the popular pontiff. He said the two spent the most time discussing the plight of the poor and the marginalized as well as regions of conflict and the elusive nature of peace around the world.

The Vatican, in a statement shortly after the meeting, said discussions centered on questions of particular relevance for the church in the U.S., “such as the exercise of the rights to religious freedom, life and conscientious objection” – issues that have fueled divisions between Obama and the church.

But Obama said those discussions took place with the Vatican Secretary of State Pietro Parolin, not with Francis. “We actually didn’t talk a whole lot about social schisms in my conversations with His Holiness,” he added. “In fact, that really was not a topic of conversation.”

“I was grateful to have the opportunity to speak with him about the responsibilities that we all share to care for the least of these, the poor, the excluded,” Obama said later during a news conference with Italian Prime Minister Matteo Renzi in Rome. “And I was extremely moved by his insights about the importance of us all having a moral perspective on world problems and not simply thinking in terms of our own narrow self-interests.”

Obama emerged visibly energized from his audience with the pope, during which he invited Francis to visit the White House.

Francis presented Obama with a copy of his papal mission statement decrying a global economic system that excludes the poor. Obama said he would keep it at the White House.

“You know, I actually will probably read this when I’m in the Oval Office, when I am deeply frustrated and I am sure it will give me strength and will calm me down,” Obama said.

“I hope,” the pope responded.