US Defense Secretary Leon Panetta said that President Barack Obama will decide in the next few weeks about the number of troops to stay in Afghanistan after the combat mission ends in 2014.
He did not reveal what options Obama is considering.
But US officials have said he may settle on a figure between 6,000 and 10,000. There currently are about 66,000 US troops in Afghanistan.
The mission after 2014 is expected to focus on counterterrorism and training of the Afghan local troops.
Panetta made the comments, reported by the Associated Press, to about 100 US service members inside an aircraft hangar at a base west of Kuwait City. He emphasised that the US is winding down its involvement in lengthy wars.
Panetta also met with top Kuwaiti government officials on Tuesday.
This is likely to be Panetta's last trip to the Middle East before he retires. He has not said publicly when he will leave but it is widely believed to be early next year.