George W. Bush has agreed to commit the US to a "general time horizon" for withdrawal of combat troops from Iraq, marking a significant shift by a president who has long opposed setting target dates for ending the war.

The president struck the agreement with Nouri al-Maliki, Iraq's prime minister, yesterday as part of negotiations over the future of US forces in Iraq.

The White House insisted the goals would be subject to continued improvement in security conditions.

The Iraqi government had been pressing Washington to commit to withdrawal dates as part of a proposed bilateral agreement to replace the United Nations' mandate that authorises US operations in Iraq.

The White House said Mr Bush and Mr Maliki agreed improving security conditions should allow for "a general time horizon" for the handover of cities and provinces to Iraqi control and further reductions in US troop levels. No dates were agreed yesterday but Baghdad has proposed that all US troops should have left the country five years after Iraqi forces take leadership of national security - a precondition that could still be years away.

A US spokesman denied the agreement represented a U-turn. "These are aspirational goals, not arbitrary timetables based on political expediency," he said.

Barack Obama, the Democratic presidential candidate, has vowed to withdraw all combat forces from Iraq within 16 months of taking office, while John McCain, his Republican rival, has pledged to keep troops there as long as necessary.

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