President Bush and Iraqi Prime Minister Nouri al-Maliki agreed Friday to include a “general time horizon” for U.S. troop withdrawals as part of a pending bilateral security agreement, the White House said.

“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 in a statement.

Bush has repeatedly rejected attempts by Democrats in Congress to impose or even recommend a timeline for Iraq withdrawal. The White House statement made clear the administration would continue to reject what it called “an arbitrary date for withdrawal.”

The agreement follows statements by Maliki and other senior Iraqi officials demanding that withdrawal timelines be included in any security pacts.

The U.N. mandate under which coalition forces operate in Iraq expires at the end of this year. The two governments have been negotiating a bilateral agreement under which U.S. forces would remain in Iraq; the withdrawal timeline would be a part of that deal, the White House said.

Bush has insisted such a deal would not need congressional approval, but Democrats have demanded a say in the agreement.

The House version of the fiscal 2008 defense authorization bill would require congressional authorization for any agreement between the United States and Iraq that obligated the U.S. military to defend Iraq. That has drawn a veto threat from the president.

The version of the defense bill approved by a Senate committee has no provision requiring congressional approval of a U.S.-Iraq pact, but Carl Levin, D-Mich., the Senate Armed Services chairman, said a similar amendment could offered when the bill comes to the Senate floor.