Bush and Benedict meet at the Vatican
Mr Bush and the Pope shook hands and posed for photographs ahead of talks in Pope Benedict's private library.
In brief exchanges, Mr Bush described the just-concluded G8 summit as a "success".
But when asked by the Pope whether the dialogue with Russian President Vladimir Putin "was also good", Mr Bush said he would answer "in a minute" - before the two men went behind closed doors.
"The worrying situation in Iraq and the critical situation of the Christian community there" were among issues discussed along with "the Middle East, the Israeli-Palestinian question and Lebanon," the Vatican said in a statement.
The two men also discussed "ethical and religious issues" including human rights and freedom of religion, "the defence and promotion of life, marriage and the family, the education of new generations and sustainable development," it said.
There was an exchange of gifts and then Mr Bush spent a few minutes with Cardinal Bertone, the Vatican Secretary of State and number two to the Pope at the Vatican, before leaving for a working lunch with Mr Prodi.
The BBC's David Willey, in Rome, says President Bush told the Pope about his plans for increasing American aid to Africa and particularly for increasing help to Aids sufferers.