US President Barack Obama has met Pope Benedict XVI for the first time, hours after the end of the G8 summit in Italy.
The two met for about 40 minutes in the pontiff's study at the Vatican.
Correspondents said the two were likely to find common ground on subjects like Middle East peace, climate change and the global economic crisis.
But they also covered areas on which they disagree, including abortion and stem cell research, reports said.
As he shook hands with the pontiff, Mr Obama said it was a "great honour" to meet him.
The US president arrived at the Vatican from the summit in the Italian city of L'Aquila, and told the Pope as he greeted him that the meeting had been "very productive".
'Eager to listen'
In a sign of the differences between the Pope and Mr Obama, the pontiff gave the president a booklet outlining the Vatican's position on issues such as abortion and embyronic stem-cell research.
The Catholic Church opposes both practices; Mr Obama overturned a ban on stem-cell research earlier this year.
They discussed a range of those issues and I think the president was eager to listen to the Holy Father
The president also supports legal abortion but regularly stresses the need to reduce the numbers of abortions carried out in the US.
He emphasised this attitude to the Pope, US officials said after the meeting.
"In the course of their cordial exchanges, the conversation turned first of all to questions which are in the interest of all and which constitute a great challenge... such as the defence and promotion of life and the right to abide by one's conscience," the Vatican said.
Denis McDonough, an aide to Mr Obama, told reporters aboard Air Force One that the discussions were respectful.
"They discussed a range of those issues and I think the president was eager to listen to the Holy Father. He is eager to find common ground on these issues and to work aggressively to do that."
There was more agreement on the issue of the Middle East, although Mr Obama reportedly emphasised that the Pope himself had an important role to play in fostering peace in the region.
Earlier this week the White House press secretary Robert Gibbs said he thought the talks would be "frank".
The BBC's David Willey reports from Rome that the Vatican has adopted a friendly tone towards the US president since his election last November, despite his change of policy from the Bush administration on funding for embryonic stem cell research.
The Vatican newspaper has gone as far to defend him against attacks by abortion rights opponents in America, asserting that he is not a pro-abortion president as some American Catholic bishops have said, our correspondent adds.
Both men have made efforts to reach out to the Muslim world. They also share views about nuclear non-proliferation and arms reductions, and helping the poor cope with the global economic crisis.
This week the Pope published an encyclical - the highest form of papal teaching - in which he argued for an ethical approach towards economic policies and in reorganising the international financial system.
He gave Mr Obama a leather-bound copy of the encyclical as they exchanged gifts following Friday's meeting.
Mr Obama gave the Pope a stole that once covered the body of John Neumann, who lived in the 19th Century and was America's first Catholic bishop to be made a saint.
Before the meeting with the Pope, Mr Obama held talks with the Vatican's secretary of state, Cardinal Tarciso Bertone.
Afterwards, he was travelling to the West African nation of Ghana.
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