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American troops must stay in the battle, Bush said, and more than 130,000 will remain after the newly ordered withdrawals are completed in July.
 
"The principle guiding my decisions on troop levels in Iraq is: return on success," the president said.
 
"The more successful we are, the more American troops can return home."
 
'Success' in Anbar
 
The president touted Anbar province as evidence of the success of the US troop "surge".
 
But his speech came just hours after Sattar Abu Risha, a key Sunni tribal leader who worked with the US against al-Qaeda in al-Anbar, was killed by a roadside bomb.
 
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Still, Bush firmly rejected calls to end the war, saying the fighters who threaten Iraq's future are also a danger to US national security.
 
He described the withdrawals, and the US forces still fighting in Iraq, as a compromise on which war supporters and opponents could agree.
 
"The way forward I have described tonight makes it possible, for the first time in years, for people who have been on opposite sides of this difficult debate to come together," Bush said.
 
"Whatever political party you belong to, whatever your position on Iraq, we should be able to agree that America has a vital interest in preventing chaos and providing hope in the Middle East," the president said.
 
Democratic reaction
 
But Democrats were not impressed.
 

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Jack Reed, a senator and former army ranger officer who delivered the Democratic response, said that "once again, the president failed to provide either a plan to successfully end the war or a convincing rationale to continue it".
 
Nancy Pelosi, the Democratic house speaker, said: "The American people long ago lost faith in the president's leadership of the war in Iraq because his rhetoric has never matched the reality on the ground.
 
"The choice is between a Democratic plan for responsible redeployment and the president's plan for an endless war in Iraq."
 
Democrats have said they would launch a new attempt in the senate next week to change the role of US forces in Iraq through legislation tied to a defence spending bill.
 
'Enduring relationship'
 
Bush also said on Thursday that the US engagement in Iraq would stretch beyond his presidency, requiring military, financial and political support from Washington.
 
He said Iraqi leaders "have asked for an enduring relationship with America. And we are ready to begin building that relationship in a way that protects our interests in the region and requires many fewer American troops".
 
Bush also acknowledged that Iraq's government had failed to meet goals for political reconciliation and security.
 
"In my meetings with Iraqi leaders," he said, "I have made it clear that they must."
 
A White House report, to be released Friday, will document the continued failures of the Iraqi government.