Saddam Hussein's regime is near collapse and the international community should do all it can to help build Iraq into a thriving democracy once the dictator is toppled, British Prime Minister Tony Blair said Tuesday.

"The power of Saddam is ending," Blair said during a joint press conference with President Bush in Belfast, Ireland.

The two world leaders offered up their assessments of the war after a meeting at Hillsborough Castle to talk about peace in Northern Ireland and in the Middle East and how to tackle a post-war Iraq.

Bush said "a new day is beginning" in Iraq, but cautioned there will be difficult fighting ahead.

"As this war has progressed the world has witnessed the brutal desperation, the true character of the Iraqi regime," Bush said. "There will be difficult fighting ahead, yet the outcome is not in doubt. Iraq will be free."

"In all parts of the country, our power is strengthening, the Iraqi regime is weakening, the Iraqi people are turning towards us," said Blair.

Late Monday night, coalition forces dropped four huge bunker buster bombs on a Baghdad building where military officials believed Saddam, his sons and other regime officials were meeting. There is a chance they all died.

"I don't know whether he survived," Bush said. "The only thing I know is that he's losing power."

In addition to showcasing military progress in Iraq, the two leaders -- holding their third meeting in three weeks -- were looking ahead to the postwar period while seeking to minimize splits on who should govern and rebuild the country.

Blair wants more U.N. involvement than Bush.

But what the two do agree on is they want to avoid a U.N. Security Council deadlock like the one they faced trying to get a resolution passed authorizing war with Iraq.

A key component of the talks Tuesday was on U.N. resolutions that would define what role the international body would play in reconstruction and governing.

"There is enough work for everyone to have a role," said Secretary of State Colin Powell.

Bush 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.

Bush has stressed that the Iraqi people will take the lead in setting up the government and having a government truly representative of their people.

"Saddam Hussein will be gone … they just need to know that," he said. "Because we're not leaving … until they're ready to run their own government."

Powell said the United Nations can lend a hand in providing humanitarian aid and adding legitimacy to the interim authority, but he didn't put forth a solid role for the international body beyond that. A Blair spokesman, stressing agreement with the United States, told reporters the United Nations doesn't want to run Iraq.

Irish Prime Minister Bernie Ahern, who joined the talks on Northern Ireland, said he would tell Bush the United Nations should have a primary role in Iraq's reconstruction.

Bush's attendance at the summit may signal his support for Blair's peace blueprint for Northern Ireland, which attempts to reconcile the region's Protestants and Catholics.

Blair is hoping the agreement could serve as a model peace roadmap for the long-standing rift between Israelis and Palestinians.

Blair has racked up IOUs from Bush by backing the president on Iraq in the face of fierce opposition at home.

Following their meeting, the two leaders planned joint statements on both Northern Ireland and Iraq.

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 so-called Good Friday accords. The pact sought to end three decades of sectarian conflict in the British territory.

"This is a very significant step in the life of Northern Ireland," Powell said.

But the Iraq war undercut support for Bush among some citizens in Northern Ireland, particularly in the most hard-line Catholic areas.

In the Bogside district of Londonderry, Northern Ireland's second-largest city, a 50-foot-high wall that for more than three decades has read: "You are now entering Free Derry," was painted solid black in a gesture of mourning for Iraqis killed in the war.

The area's veteran civil rights activist, Eamonn McCann, said most Derry Roman Catholics consider Bush a hypocrite for telling the Irish Republican Army -- the region's main militant group -- that violence doesn't pay.

"Bush is saying to political leaders here: Give up the gun, don't use violence to pursue political ends, follow the rule of law. He is demanding that they do that even as he prosecutes the war in Iraq," McCann said. "I doubt if I've ever encountered anything as grotesquely hypocritical as the exercise in Hillsborough."

Fox News' Wendell Goler and The Associated Press contributed to this report.