WASHINGTON — Rejecting calls to leave Iraq, President Bush yesterday ordered gradual American troop reductions from their highest level of the war and said more forces can come home as progress is made. At the same time, he said Iraq needs “an enduring relationship with America.”

In remarks prepared for a primetime address from the Oval Office, Mr. Bush presented his strategy for reducing American forces. “The principle guiding my decisions on troop levels in Iraq is: return on success. The more successful we are, the more American troops can return home.”

With no dramatic change in course, Mr. Bush’s decision sets the stage for a fiery political debate in Congress and on the 2008 presidential campaign trail. Democrats said Mr. Bush’s approach was unacceptable.

Senator Reed of Rhode Island, a former Army Ranger 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.”

Mr. Bush approved the recommendations of the top American commander in Iraq, General David Petraeus, to withdraw five combat brigades — at least 21,500 forces — and an undetermined number of support troops by July. The reductions represented only a slight hastening of the originally scheduled end of the troop increase announced in January. The White House said 5,700 troops would be home by Christmas.

Mr. Bush’s speech was the latest turning point in a 4 1/2-year-old war marred by miscalculations, surprises, and setbacks.

Almost since the fall of Baghdad, in April 2003, American commanders and administration officials in Washington mistakenly believed they were on track to winding down America’s involvement and handing off to the Iraqis. Instead, the insurgency intervened, and the reality of a country in chaos conspired to deepen the American commitment.

Mr. Bush said the American engagement 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.”

Mr. Bush said his strategy — leaving about 130,000 American soldiers in Iraq to continue fighting — bridges the desires of people who want to bring troops home and those who believe that success in Iraq is essential to America’s security.