At least three options are now under consideration, according to officials at the White House, the Pentagon and the State Department. One plan, backed by Thomas E. Donilon, the national security adviser, would be to announce that at least 10,000 more troops would come home by the end of December, and then 10,000 to 20,000 more by June 2013.

Vice President Joseph R. Biden Jr. has been pushing for a bigger withdrawal that would reduce the bulk of the troops around the same time the mission shifts to a support role, leaving behind Special Operations teams to conduct targeted raids. Mr. Biden has long said that the United States mission in Afghanistan is too broad and should focus primarily on a narrow counterterrorism mission against insurgents seeking to attack the United States.

Mr. Obama’s military commanders, meanwhile, want to maintain troops in Afghanistan as long as possible. If cuts have to be made, the commanders favor making them at the end of 2013, after the fighting season is largely finished. Any troop cuts made midyear would mean that those forces would not be available during the main fighting season, which runs from spring to early fall.