The United States and Iraq have agreed to seek "a general time horizon" for further withdrawals of American troops from the war.

The White House says President Bush and Iraqi Prime Minister Nouri al-Maliki said the timing of troop reductions should be part of a broader security agreement being negotiated between Washington and Baghdad. It described troop withdrawals as one of several "aspirational goals."

The White House says the goals would be based on continued improvements on the ground in Iraq and would not be an arbitrary date for withdrawal.