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The capture of Saddam Hussein (search) was a significant political coup for President Bush (search), who had been facing mounting doubt over his administration's decision to go to war with Iraq.

"It should now be clear to all: Iraq is on the path to freedom," a beaming Bush told a news conference on Monday. "In 2003, we've become a safer, more prosperous and better nation. ... We will stay the course until the job is done."

With an increasing number of U.S. military casualties and continued volatility in the region since the official end of combat in May, criticism of the Bush administration had been growing and his political future seemed shaky. But Saddam's successful capture on Saturday changed all that.

The pictures told the stark story of the victor and the vanquished: A triumphant Bush proclaimed the end of a "dark and painful era" in Iraq, while a haggard-looking Saddam was being examined by a doctor who probed his mouth with a tongue depressor.

When asked if he had a message to send to Saddam, Bush said: "Good riddance. The world is better off without you, Saddam Hussein."

Bush said that while he has his own personal views about what punishment Saddam deserves, he favors letting the Iraqis decide what to do with their former dictator.

"We will work with Iraqis to develop a way to try him that will withstand international scrutiny," Bush said. "He needs to be brought to justice. There needs to be a public trial."

For months, Saddam's ability to remain at large despite one of the world's biggest manhunts had been a blow to U.S. prestige and claims of progress in Iraq.

"As long as he was out there running around, it made us look like we were more bark than bite," said Rick Barton, senior adviser at the Center for Strategic and International Studies (search).

The persistent violence and growing death toll of American soldiers had opened the way for criticism that Bush lacked a postwar strategy for restoring stability in Iraq. Americans wearied of scenes of homicide bombings and flag-covered coffins at funerals, and the polls showed the nation was evenly split on approval of Bush's handling of Iraq.

But with Saddam's capture, many critics were silenced, at least for the moment, and Bush was expected to get a big boost in the polls as he moves into a re-election year.

"The Democrats can't touch him at the moment," said Columbia University historian Henry Graff. "He said he was going to get him. He got him. What more do you want? Now if we can lower the level of violence over there, he's going to look good."

Bush, in an address to the nation, cautioned that there would be more bloodshed.

"The capture of Saddam Hussein does not mean the end of violence in Iraq," Bush said. "We will face terrorists who would rather go on killing the innocent than accept the rise of liberty in the heart of the Middle East."

A central question will be how much control Saddam exerted over Baath Party (search) loyalists believed responsible for the daily attacks. The way he was captured, alone at the bottom of a pit at a farmhouse, did not leave the impression of a man in charge.

Democratic presidential candidates, divided between pro- and anti-war positions, found consensus by saying it was a great day for U.S. soldiers, the people of Iraq and the world — omitting praise for the president.

"This is a huge victory for Bush. It's clear by getting Saddam early, bringing him to trial, the president can send out a message that he's winning the war on terror," said Democratic strategist Donna Brazile, who managed Al Gore's (search) 2000 campaign.

Bush's allies expect that Democrats to regroup and go after the president another way.

"Politicians are pretty smart," Senate Majority Leader Bill Frist (search) said on "Fox News Sunday." "They'll go out and try to pick another issue. They'll look at any incident that happens in the next week and maybe even diminish the capture of Saddam Hussein."

Bush himself told reporters on Monday that he "looks forward to the political debate later on."

"I look forward to making my case," the president said.

More homicide bombings and more coffins could put Bush back on the defensive. "Nobody can predict what's going to happen over the next month," Frist said, "so there'll be plenty of fodder for them to go after."

Saddam's capture was a particularly sweet moment for the Bush family, father and son presidents who confronted the Iraqi leader in two wars and wound up being criticized for letting him get away. The two Bushes were together at the White House on Friday but went their separate ways over the weekend.

Even some of Bush's harshest critics overseas were forced to offer congratulations, most notably the leaders of France and Germany, who had opposed the war and refused requests for troops and money for Iraq's reconstruction.

"It's a major event that should strongly contribute to democracy and stability in Iraq and allow the Iraqis to master their destiny," said French President Jacques Chirac (search).

For a while, at least, Saddam's capture should ease global criticism of the United States.

"It's clearly going to be helpful because it does deal with this growing impression of being somewhat ineffectual that had been developing over the last several months," said Barton. "It re-establishes that the United States is a capable player, capable of taking care of somebody like Saddam Hussein."

Bush on Monday characterized the rift between the U.S. and countries like France and Germany as a "disagreement," not a lasting break in relations.

"I don't agree that this is a dividing line," he told the news conference. "I think this is a disagreement on this particular issue. We can work together on other issues."

Bush also said the United States came to this moment "through patience and resolve and focused action."

"Our security is assured by our perseverance and by our sure belief in the success of liberty. And the United States of America will not relent until this war is won."

Fox News' Catherine Donaldson-Evans and The Associated Press contributed to this report.