July 18 (Bloomberg) -- President George W. Bush and Prime Minister Nuri al-Maliki have agreed that a ``general time horizon'' is needed for the reduction of U.S. combat troops in Iraq.

The two leaders, speaking yesterday by video conference, ``agreed that improving conditions'' in Iraq should permit setting ``a general time horizon'' for further draw-downs of U.S. forces, spokeswoman Dana Perino said in a statement.

The time horizon would be included in agreements now under negotiation that would define the U.S. role in Iraq and the status of American forces there, she said.

Bush and Maliki agreed that any decisions on troop reductions would be based on ``continued improving conditions on the ground and not an arbitrary date for withdrawal,'' Perino said. She described the draw-downs as among the leaders' ``aspirational goals'' and said another objective was the resumption of Iraqi security control over the nation.

Maliki last week called for the agreements to include a timetable for the withdrawal of U.S. forces. American officials initially rejected that demand.

A White House spokesman, Gordon Johndroe, said the new statement doesn't reflect a shift in the U.S. position.

An Iraqi government spokesman, Ali al-Dabbagh, said the goal of an agreement would be to ``decrease the number of American forces in Iraq and later withdraw them,'' Agence France-Presse reported.

Election Issue

The question of U.S. withdrawals is a matter of debate in the U.S. presidential campaign. The presumptive Democratic nominee, Senator Barack Obama of Illinois, has said he would pull most American combat troops from Iraq within 16 months of taking office.

Obama's Republican counterpart, Senator John McCain of Arizona, rejects a timetable for withdrawal and says U.S. forces must remain for as long as necessary to stabilize the country.

U.S. forces are in Iraq under a United Nations mandate that expires December 31. Scott Stanzel, another White House spokesman, said the U.S. and Iraq still have the goal of reaching a new bilateral agreement by July 31.

``We have reached a point in Iraq where we can have these discussions,'' Stanzel said. They are discussing ``aspirational goals, not arbitrary timelines based on political expedience,'' he told reporters traveling with Bush in Tucson, Arizona.

There are about 150,000 U.S. troops in Iraq, according to the Defense Department. The last of five American brigades sent last year as part of an increase of forces is due to return home this month.

The chairman of the Joint Chiefs of Staff, Admiral Michael Mullen, said earlier this week he expects to be able to call for new draw-downs this fall. The outgoing commander of U.S. forces in Iraq, General David Petraeus, is due to make a recommendation on that issue sometime in September.

To contact the reporter on this story: Roger Runningen in Washington at rrunningen@bloomberg.net; Ken Fireman in Washington at kfireman1@bloomberg.net

Last Updated: July 18, 2008 13:18 EDT