Known for not getting his news from television, President Bush intermittently watched events unfold in Baghdad Wednesday as Iraqis, assisted by U.S. Marines, pulled down a statue of Saddam Hussein in the city's central square.

"They got it down," was the president's response after seeing the statue pulled to the ground. The president's observation came after a morning of meetings with his national security team, Secretary of Defense Donald Rumsfeld and Slovak President Rudolph Schuster.

But the White House is still reacting with "utmost caution" and is currently observing how the Iraqi people are responding to their newfound freedom, even as Iraq's ambassador to the United Nations Mohammad Al-Douri told reporters, "The game is over .. the war I mean." Al-Douri also said he no longer has any communication with Saddam.

Rumsfeld responded by saying that the war was never a game nor is it over yet.

The administration is trying to avoid getting into the same debate with reporters about the speed of victory, and is doing its best not to remind them that a little more than a week ago they were asking why coalition forces seemed to be bogged down.

Speaking to the American Society of Newspaper Editors, Vice President Cheney refrained from saying "I told you so."

"In the early days of the war the plan was criticized by some retired military officers embedded in TV studios. But with every day and every advance by our coalition forces, the wisdom of that plan becomes more apparent," Cheney said.

"The conclusion of the war will mark one of the most extraordinary military campaigns ever conducted. It's proceeded according to a carefully-drawn plan with fixed objectives and flexibility in meeting them."

Even some who have questioned the administration's actions in Iraq expressed pleasure with the unfolding events in Baghdad.

"American troops have done an extraordinary job in Iraq, and all of America should be proud of their selfless service to country. Saddam Hussein made a grave error when he chose to make war the ultimate weapons inspections enforcement mechanism," said Democratic presidential hopeful Sen. John Kerry.

Instead of declaring victory on Wednesday, aides say the president knows the war is not over and that great dangers could lie ahead, particularly as not all the cities have yet been wrested from Saddam's regime's control. Forces continue to fight in Saddam's hometown of Tikrit.

Cheney, like other officials, warned that "we must expect vicious tactics until the regime's final breath."

Press Secretary Ari Fleischer said the pictures from Baghdad show "mankind's desire to live free" and that the president always knew the Iraqi people would welcome coalition forces as liberators once they knew Saddam's grip on the country was truly gone.

It is still unclear whether Saddam is alive or dead, but the administration dismissed reports Wednesday that the Iraqi despot had taken refuge in the Russian embassy.

Rumsfeld said that he believes that Saddam "is either dead or incapacitated or he is healthy and cowering some place, trying to avoid being caught."

The defense secretary also issued a veiled warning to Syria for apparently allowing leaders of the old regime to slip across the border.

Military officials have acknowledged that the fighting is coming to a conclusion and debate has begun over when the president might want to declare a coalition victory and move to implementation of postwar plans.

The president so far has kept a low profile, trying to prevent any appearance of bravado and mindful of anti-American sentiment in the Arab world. But the United States is insistent that the coalition lead any postwar reconstruction efforts and has repeatedly promised not to abandon the Iraqi people.

"To those Iraqi people who are not yet free, let me assure you that you will be free. I've seen President Bush almost every day since this conflict began, and I can assure you that he is, like the American people, committed to your freedom and to your future and to seeing this effort through," Rumsfeld said.

U.S. officials rejected overnight calls from Russia, France and Germany to give the United Nations control of post-Saddam Iraq after the fighting ends.

The three countries released a joint statement saying "the U.N. alone" should have a role in reconstructing Iraq. Fleischer rejected that as "an exclusionary notion" and said it would be pleasant if the three nations could express more concern for the Iraqi people.

"I would hope that rather than focus on what the U.N. alone should have as a role in [rebuilding Iraq], it would be nice if these people would talk about ... the Iraqi people first," Fleischer said. "That would be a nice message to hear from Moscow, a statement about the Iraqi people first."

The administration said the United Nations should play a "vital role" in rebuilding Iraq, but the president has suggested its participation should be strictly limited to humanitarian assistance, fund-raising and making suggestions about the makeup of the interim authority.

State Department Spokesman Richard Boucher was reluctant to make predictions about how the United Nations would go about withdrawing recognition of Saddam's regime and welcoming a new government.

"Exactly at what point it becomes appropriate to have a new group of Iraqis representing Iraq at the United Nations is, of course, something that needs to be addressed. I don't think we're quite at that point," Boucher said.

As for Iraqi ambassador Al-Douri's legal status at the United Nations, Boucher was vague.

"We've never considered him very credible or a reliable representative of Iraq, I'd have to say, certainly not of the Iraqi people," he said.

In addition, it's likely that for the United Nations to take a primary role in an interim government would require a Security Council resolution, one that the United States and Great Britain might be loathe to approve after meeting such resistance from the Council before the war.

"We don't believe that the United Nations is equipped to play that central role," Cheney told the ASNE.

Fox News' Wendell Goler, Jim Angle and Teri Schultz contributed to this report.