WASHINGTON D.C. — The number of U.S. troops in Afghanistan may drop well below 10,000 - the minimum demanded by the U.S. military to train Afghan forces - as the longest war in American history winds down, Obama administration officials briefed on the matter say.

Since Afghanistan's general election on April 5, White House, State Department and Pentagon officials have resumed discussions on how many American troops should remain after the current U.S.-led coalition ends its mission this year.

The Obama administration has been looking at options for a possible residual U.S. force for months.

There are now about 33,000 U.S. troops in Afghanistan, down from 100,000 in 2011, when troop numbers peaked a decade into a conflict originally intended to deny al Qaeda sanctuary in Afghanistan after the September 11, 2001, attacks.

Results of the recent Afghani presidential election may not be known for weeks, or months if runoffs take place. But leading candidates have said they will sign the agreement, which has been on hold because of reservations from current Afghan President Hamid Karzai.

In late February, Obama announced that the United States might seek to sign the deal with Karzai's successor and possibly keep troops there after 2014 to train and advise Afghan forces and pursue al Qaeda militants.

Some U.S. officials believe Afghan forces will require substantial, hands-on support from foreign troops, in addition to help from the United States.