But White House spokeswoman Dana Perino said Friday any reduction in the US force presence "would be based on continued improving conditions on the ground and not an arbitrary date for withdrawal."

Bush’s concession reflects both progress in stabilizing Iraq and the depth of political opposition to an open-ended military presence in Iraq and at home.

The agreement, announced in coordinated statements released Friday by the White House and Maliki’s government, reflected a significant shift in the war in Iraq.

The two leaders, speaking by videoconference Thursday, also settled on a "common way forward" in stumbling talks to craft a long-term pact governing diplomatic ties and the US military presence, the White House added.

Bush, an unpopular president waging an unpopular war in the twilight of his tenure, has adamantly opposed setting a schedule for scaling back U.S. forces, even as Democratic presidential candidate Barack Obama has vowed, if elected, to withdraw troops in 16 months.

DEAL AIMED AT END-MONTH

U.S. and Iraqi negotiators have been working in fits and starts on a formal Status of Forces Agreement to provide a legal basis for U.S. troops to remain when an U.N. mandate expires at the end of the year.

Maliki, expressing his government's growing confidence as violence has decreased, last week raised the prospect of setting a timetable for U.S. troop withdrawal. But U.S. officials have been more cautious.

The White House said Bush and Maliki aimed to complete a deal by the end of the month. "The president and the prime minister agreed that improving conditions should allow for the agreements now under negotiation to include a general time horizon for meeting aspirational goals -- such as the resumption of Iraqi security control in their cities and provinces and the further reduction of U.S. combat forces from Iraq," the White House said.