HILLSBOROUGH, Northern Ireland - Determined to display unity, President Bush and British Prime Minister Tony Blair said here yesterday that they envision "a vital role" for the United Nations in rebuilding Iraq, but seemed unable to agree on how large a role it should play.

The president said the United Nations would be "suggesting" --- but not choosing - leaders to serve on a new interim Iraqi authority that will hold power until a permanent government is in place. Blair had been pressing Bush to give the international body a more prominent role, but does not appear to have made much headway.

"The important thing is not to get into some battle about words of the precise role here or there," the prime minister said at a joint news conference with Bush at the small castle outside Belfast where they conferred.

Wrapping up their two-day summit, Blair said, "Let's all just agree that the basic things that the Iraqi people want is they want to have a country where they are able to exploit their own wealth for their own prosperity, where they have basic protection of human rights and where they have a government genuinely representative of Iraqi people."

The president, seeking to dispel concerns that the Americans and the British will dominate postwar Iraq, said, "I hear a lot of talk here about how we're going to impose this leader or that leader. Forget it. ... The Iraqis are plenty capable of running Iraq and that is precisely what is going to happen."

In addition to Iraq, the two leaders discussed the Middle East conflict, and Bush offered strong support to Blair's effort this week to revive a stalled peace process for Northern Ireland.

But with military advances in Iraq crippling Saddam Hussein's regime and a U.S. team preparing to enter the country to begin laying the groundwork for a new government, postwar Iraq dominated the conversations. Disagreement over the role of the United Nations in the aftermath of the war has in recent weeks complicated the close wartime alliance between Bush and Blair.

Bush sought to portray himself as in tune with Blair yesterday, but they have different priorities. The president said that he envisions the international body providing mostly food, medicine and other aid in Iraq. But he made clear that he is still committed to a plan in which a Pentagon-run agency will control the country in the immediate aftermath of war and work closely with a new interim governing authority composed of Iraqis from within and outside the country.

"When we say vital role for the United Nations, we mean vital role for the United Nations in all aspects of the issue," Bush insisted. "Whether it be humanitarian aid, or whether it be helping to stand up an interim authority."

Blair, echoing leaders from Russia, France and Germany, has been pressing Bush to give the United Nations a larger role. The prime minister also has been trying to mend relations with those countries and others that vehemently opposed military action, but are now calling for the United Nations to assume a "central role" in Iraq in the aftermath of the conflict.

In a joint statement released yesterday, Bush and Blair said they would seek new U.N. Security Council resolutions endorsing an "appropriate post-conflict administration" for Iraq, but offered no specifics. The statement said the leaders "welcome" U.N. Secretary-General Kofi Annan's appointment of a special adviser to Iraq, but said nothing about what the adviser's role may be.

At the United Nations, the Associated Press reported that questions persist about the organization's role. "I don't think we have a clearer sense of what that role might be," said Fred Eckhard, Annan's spokesman. "It would be in everyone's best interest if the international community were brought to play in the establishment" of a postwar Iraqi government or authority.

While war successes have been a boost to Bush and Blair, how they manage Iraq afterward could be as politically risky for both leaders as the conflict itself.

Meeting for the third time in less than a month, the leaders heaped praise on each other and played up areas where they could agree.

Bush said he made the trip in part to lend support to Blair at a crucial moment in the Northern Ireland peace process. For several decades, violence ravaged this province, as Catholics and Protestants fought over whether Northern Ireland should be part of Ireland or the United Kingdom.

This week is the fifth anniversary of the Good Friday Agreement that set up a framework in which both sides would participate in a power-sharing government. There has been far less violence here since the pact was signed. But the process has bogged down over demands that the paramilitary groups involved in the bloody conflict disarm, and Blair is expected this week to propose a plan to ensure the agreement does not crumble.

The president and prime minister, after their exchange with reporters, met with Irish Prime Minister Bertie Ahern. Later, those three leaders met with key leaders from both sides of the troubles in Northern Ireland. Bush returned to Washington last night.

Bush and Blair sought to use successful efforts to curb violence in Northern Ireland as a reason to hope that the Israeli-Palestinian conflict can one day be solved.

"Here we are, for all the difficulties in Northern Ireland, able to point back to real improvements in the security and standard of living of people here," Blair said. "And to point forward to turning progress into lasting change, lasting security and lasting peace."

Bush saw successes here serving as an example to other regions afflicted with internal strife. "When the peace process is successful here, it will send a really important signal to other parts of the world," he said.

The leaders met as anti-war protestors gathered in Belfast, a half-hour away from Hillsborough Castle. Lines of armored police vehicles sat outside tiny coffee shops and bookstores. Noisy helicopters patrolled above a sun-splashed castle where flowers were blooming.

While seeking to bridge differences over the United Nations, Bush and Blair appeared confident and satisfied by recent military successes - a far cry from 12 days ago, when they met at Camp David and were hammered by questions about whether the war effort has run up against stiffer than expected Iraqi resistance.

Both leaders praised the performance of their armed forces and said Hussein's regime was all but finished.

"That grip I used to describe that Saddam had around the throats of the Iraqi people are loosening," Bush said, holding up both hands as if he were gripping someone's neck. "I can't tell you if all 10 fingers are off the throat, but finger by finger, it's coming off."

Blair and Bush together made the case for war by arguing that Hussein possesses weapons of mass destruction that he might use, or pass to terrorists. Though there have been no confirmed findings of such weapons, Blair said yesterday that "we know the regime has them."

"As the regime collapses," Blair said, "we will be led to them."