VATICAN CITY (Reuters) - Calling himself "a great admirer", President Barack Obama held nearly an hour of private talks about the global situation with Pope Francis on Thursday and invited the pontiff to visit the White House.
Obama appeared at ease and joked with the pope during the parts of their first meeting that were open to reporters, at one saying he did not know how his wife and children "put up with me".
The president and his delegation, including Secretary of State John Kerry, walked past the frescoed halls of the Vatican's Apostolic Palace to the entrance of the Francis' private library.
There were no immediate details of what they discussed, but in the run up to the meeting, Obama had given an interview to an Italian newspaper praising the pope's commitment to addressing growing gaps between rich and poor.
"It is a great honour. I'm a great admirer," the president said as the pope greeted him and they sat at the pontiff's desk. "Thank you so much for receiving me."
Obama invited the pope to visit the White House as he was giving Francis a symbolic gift of seeds of fruit and vegetables from the garden of the presidential residence.
The White House said other seeds would be donated in the United States that will yield several tons of produce to a charity of Pope Francis' choosing.
"If you have a chance, you can come to the White House and you can see the garden," Obama said to the pope as he was explaining the gift to the pope.
The Pope, responding in Spanish, said "Como no?" (For Sure!)
The pope gave Obama two commemorative medals and a red leather-bound copy of Evangeli Gaudium (The Joy of the Gospels), a document Francis wrote last year which is seen as the road map for his papacy.
"You know, I will probably read this in the Oval Office when I am deeply frustrated and I am sure that it will give me strength and calm me down," Obama said. The pope responded in English: "I hope".
In another moment of levity during the audience, after the delegation was being shown to their seats and pictures were being taken, Obama told the pope's translator: "His Holiness is the only person who has to put up with more protocol than me."
Ahead of the meeting, Obama told the Corriere della Sera that Francis's "great moral authority" had added weight to calls to redress the increasing imbalance between the winners and losers of globalisation and economic change.
"In the United States over the last few decades, we've seen a growing gap between the income of those at the very top and the income of the typical family," he said.
"But this isn't just a problem for the United States, it's a problem for countries around the world. And it isn't just an economic issue, it's a moral issue."
As he arrived at the Vatican, Obama was greeted by Archbishop Georg Ganswein, Prefect of the Pontifical Household, together with a detachment of the ceremonial Swiss Guard.
Francis has turned his back on much of the traditional formality of the Vatican but he deployed the full weight of state ceremonial on Thursday, welcoming the U.S. President outside the Papal Library in the richly frescoed Small Throne Room, where they shook hands warmly before beginning their private meeting.
Since his election a year ago, Pope Francis has several times criticised unbridled capitalism, the excesses laid bare by the global financial crisis, and the growing gap between the rich and poor, even in developed countries.
Obama has repeatedly praised the pope for his compassion and emphasis on helping the poor, and the meeting could help to give impetus to some of his initiatives back home, such as boosting the middle class and helping low-income Americans succeed.
(Additional reporting by James Mackenzie; Editing by Kevin Liffey and Susan Fenton)