Story Highlights• NEW: Democrats welcome news of Hussein's death
• President cites Iraqis' "resolve to move forward"
• Remarks acknowledge challenges ahead
• White House says Bush was asleep when Hussein was executed
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WASHINGTON (CNN) -- President Bush, able to claim few victories in the war in Iraq, issued a satisfied but measured statement about 90 minutes after former Iraqi dictator Saddam Hussein was executed.
"Fair trials were unimaginable under Saddam Hussein's tyrannical rule," the president said. "It is a testament to the Iraqi people's resolve to move forward after decades of oppression that, despite his terrible crimes against his own people, Saddam Hussein received a fair trial. This would not have been possible without the Iraqi people's determination to create a society governed by the rule of law."
The White House said Bush was asleep at the time of the execution but was briefed by national security adviser Stephen Hadley before going to bed.
In his statement, the president acknowledged that things have not gone well since Hussein was chased from power by coalition forces in 2003.
"Saddam Hussein's execution comes at the end of a difficult year for the Iraqi people and for our troops," he said. "Bringing Saddam Hussein to justice will not end the violence in Iraq, but it is an important milestone on Iraq's course to becoming a democracy that can govern, sustain, and defend itself, and be an ally in the war on terror."
The president praised the troops fighting the war and expressed optimism tempered by the reality of sectarian fighting and political problems in the United States and in Iraq.
"We are reminded today of how far the Iraqi people have come since the end of Saddam Hussein's rule -- and that the progress they have made would not have been possible without the continued service and sacrifice of our men and women in uniform," he said.
"Many difficult choices and further sacrifices lie ahead. Yet the safety and security of the American people require that we not relent in ensuring that Iraq's young democracy continues to progress."
Democrats also welcomed the news of Hussein's death. "Iraq has closed one of the darkest chapters in its history and rid the world of a tyrant," said Joseph Biden of Delaware, incoming chairman of the Senate Foreign Relations Committee.
Sen. Edward Kennedy, Democrat of Massachusetts, called Hussein "a brutal tyrant and murderous dictator."
"Now it is time for the people of Iraq to work to reconcile their differences and to heal the wounds of the past," he said. "Only that process will end the violence that has prevented Iraq from moving forward."
President Bush said, "Fair trials were unimaginable under Saddam Hussein's tyrannical rule."