The US and the EU have pledged strong support to the new Iraqi government ahead of the 30 June transfer of power.
It is Mr Bush's first official visit to the Irish Republic
The leaders issued a joint statement at the end of a summit in Ireland saying Baghdad needed the world's backing if Iraq was to become a democratic nation.
The move shows that the US and European nations have put their disagreements on Iraq aside, correspondents say.
The summit also covered trans-Atlantic trade issues, the crisis in Sudan and Iran's nuclear programme.
The meeting at Dromoland Castle, in County Clare, was the first between the US and the EU since the latter's expansion to 25 members in May.
Tight security was in place involving Irish police backed by troops, ships and 700 US security personnel.
On Saturday morning, Mr Bush held talks with Irish President Mary McAleese and Prime Minister Bertie Ahern, whose country holds the rotating EU presidency, before meeting other EU leaders.
In the joint statement, the leaders pledged to help reduce Iraq's huge foreign debt and train security forces.
Relations between the US and the bloc have been damaged by differences over the Iraq war and Middle East conflict.
Demonstrations by thousands of people against President Bush's arrival took place on Friday near Shannon airport, in the capital, Dublin, and in several other towns, but passed off peacefully.
Later on Saturday, President Bush will travel to Turkey to attend a Nato summit.
'Difference of opinion'
Mr Bush gave a clue as to how he will approach the Iraq issue when he told an Irish television interviewer that the US had made the world a safer place and deserved to be judged on its values, not on how some of its soldiers had treated prisoners, the BBC's Kevin Connolly in County Clare says.
The security operation is the largest in Irish history
"Most of Europe supported the decision in Iraq. Really what you're talking about is France, isn't it? And they didn't agree with my decision. They did vote for the UN Security Council resolution," Mr Bush said.
"We just had a difference of opinion about whether, when you say something, you mean it," he added.
Experts say that, with presidential elections looming in November, the Bush administration is keen to shore up international support for its presence in Iraq.
Domestic opinion polls show declining support for the Iraq occupation, as a succession of deadly bomb attacks overshadow the planned transition of power.
The president's visit has triggered anti-war protests
National Security adviser Condoleezza Rice, who is travelling with the president said Mr Bush "looks forward to the visit to Turkey, the opportunity to strengthen our strategic partnership with a leading secular democracy within the Muslim world".
She said the Nato summit will discuss the alliance's work in Afghanistan, where it has a contingent of peacekeeping troops.