"The hostilities phase is coming to a conclusion," said Secretary of State Colin Powell, accompanying Bush aboard Air Force One to this British territory with its own decades-old history of violence.
"It's time for all of us to think about the post-hostility phase - how we create a representative government consisting of all elements of Iraqi society," he said.
Scheduled to be on European soil less than 24 hours, Bush arrived in time for a working dinner with the British prime minister at an 18th century Georgian-style castle outside Belfast. Anti-war protesters clogged Hillsborough's tree-lined avenues.
Police shut down a major highway and a small airport in Belfast on Monday because of two bomb threats, hours before Mr. Bush was to arrive in Northern Ireland for the summit.
Mr. Bush's plans were not affected by the threats because he was not scheduled to use the highway and flew into a different airport.
Irish Prime Minister Bertie Ahern was joining the pair for talks Tuesday.
Looking beyond the fighting, Powell said the U.S.-led military coalition should control the postwar process because its soldiers have "paid the costs in lives."
That kind of talk rankles U.N. allies who oppose the war but want a hand in rebuilding oil-rich Iraq. Even Blair, the president's closest wartime ally, is pushing Bush to give the United Nations a prominent role in postwar Iraq, arguing the move would add legitimacy to the process.
Blair, under pressure in Britain for backing Bush's push to war, also was using the summit to focus the president's attention on two issues much of Europe says the administration has neglected: the troubled peace processes of the Northern Ireland and the Middle East.
Catholics, who almost universally praised the intervention of Bush's predecessor Bill Clinton in brokering peace here, simultaneously welcomed and criticized Bush for staging an Iraq war summit in their divided homeland.
"I'm very mindful that there are contradictions," said Sinn Fein leader Gerry Adams. He accused Bush and Blair of using "the Irish peace process as a stage or as a prop."
Indeed, U.S. and British officials said Iraq was dominating the talks.
Almost alone among world leaders, Bush and Blair sought to secure United Nations approval to forcefully disarm Iraq, and then waged war when their diplomacy failed. Now the two staunch allies hope to resolve - or at least paper over - their differences on Iraq's fate once the shooting stops.
Powell said little divided the leaders.
"There is enough work for everyone to have a role," Powell said, even as aides conceded privately that Blair seems to want a more influential U.N. role than Bush favors.
Bush has said he supports a U.N. role and the creation of an interim governing authority for Iraq. But he has not provided key details, such as the exact nature of the U.N.'s role and the makeup of the authority.
Powell said the United Nations can provide humanitarian aid and add legitimacy to the interim authority, but he did not offer a role for the international body beyond that. A Blair spokesman, stressing agreement with the U.S., told reporters here the United Nations has never expressed a desire to run Iraq.
Ahern said he would tell Bush the United Nations should have a primary role in Iraq's reconstruction.
"We want to see a new administration that will have greater legitimacy if it is under the (authority) of the international community," he told reporters in Dublin.
The White House has created a Pentagon office headed by a retired Army lieutenant general to administer Iraq for at least a few months. Once security is assured in Iraq, the office plans to transfer power to an interim Iraqi authority that would act as a transition to some form of democratic government.
Powell said the United States is sending a team to Iraq this week to begin laying the groundwork for an interim authority.
Administration officials say it may take two years before Iraq is ready for full self-rule.
The talks were the third face-to-face meeting in less than a month for Bush and Blair, who speak almost daily by telephone.
By heeding Blair's call for a summit, Bush took the boldest step of his presidency into the decades-old conflict in Northern Ireland.
Former President Clinton made three trips to the region, the first of any U.S. president. Bush has shown less interest than Clinton, delegating the peace process to a senior State Department official.
Blair hopes presidential backing will strengthen his hand when he publishes his government's new Northern Ireland plans by Thursday, the fifth anniversary of the Good Friday accords. The pact, forged with the help of a Clinton envoy, sought to end three decades of sectarian conflict in the British territory.
The visit demonstrates Bush's support of Blair's approach, White House officials said.
Mr. Bush and Blair also are trying to breathe new life into the peace process between Israel and the Palestinians. Blair has previously held up the progress in Northern Ireland in recent years as a model to inspire peace in the Middle East.
White House spokesman Ari Fleischer said there are no plans to release Bush's long-sought "road map" for Middle East peace during the meeting.
The United States, the European Union, the United Nations and Russia -- which make up the quartet of Mideast mediators -- have presented Israel and the Palestinians with several drafts. Both sides have made changes, but British and U.S. officials said recently that the final draft would have to be accepted as is.
The United States and Britain have said the guidelines would be unveiled after the new Palestinian Prime Minister, Mahmoud Abbas, and his Cabinet are sworn in, probably sometime this month.