WASHINGTON, July 18 (Reuters) - President George W. Bush and Iraqi Prime Minister Nuri al-Maliki have agreed that a security deal under negotiation should set a "time horizon" for meeting "aspirational goals" for reducing U.S. forces in Iraq, the White House said on Friday.

In the closest the Bush administration has come to acknowledging the likelihood of some kind of timetable for future U.S. troop cuts, the White House said "the goals would be based on continued improving conditions on the ground and not an arbitrary date for withdrawal."

Iraqi and U.S. officials 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 had recently suggested a timetable be set for U.S. withdrawal, but U.S. officials have been much more cautious despite an improving security situation.

"In the area of security cooperation, 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. (Reporting by Matt Spetalnick; Editing by Kristin Roberts)

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