President Bush has said he stands ready to help in the Northern Ireland political process.
It is Mr Bush's first official visit to the Irish Republic
He was speaking during a press conference at Drumoland Castle in County Clare following the US EU summit.
Mr Bush said he viewed the Northern Ireland process as a model for conflict resolution and it was a very important issue for his administration.
"I am fully aware that the prime minister of both Great Britain and Ireland are going to advance the process this early September," said the president.
"We stand ready to help - I wish them all the best.
"When this conflict is resolved, it will be an example for others - that long-simmering disputes can be put behind them and free societies and peaceful societies can emerge for the interest of the peoples which have been involved in those disputes."
Irish Prime Minister Bertie Ahern said he also brought the President up to date with the latest efforts to revive a power-sharing administration in Northern Ireland.
"I briefed President Bush on recent developments in the peace process,
including my discussions in London yesterday with Tony Blair," he said.
The security operation was the largest in Irish history
"We also discussed the situation of undocumented Irish immigrants in the
During the summit, the US and the EU pledged strong support to the new Iraqi government ahead of the 30 June transfer of power.
The leaders issued a joint statement at the end of the summit, 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 Mr 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.
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.
"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.