WASHINGTON -- 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 decision to consider a small force, possibly less than 5,000 U.S. troops, reflects a belief among White House officials that Afghan security forces have evolved into a robust enough force to contain a still-potent Taliban-led insurgency. The small U.S. force that would remain could focus on counterterrorism or training operations.

That belief, the officials say, is based partly on Afghanistan's surprisingly smooth election, which has won international praise for its high turnout, estimated at 60 percent of 12 million eligible voters, and the failure of Taliban militants to stage high-profile attacks that day.

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

"The discussion is very much alive," said one U.S. official who asked not to be identified. "They're looking for additional options under 10,000" troops.

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-Qaida sanctuary in Afghanistan after the Sept. 11, 2001, attacks.

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With British and other foreign troops scheduled to depart in lock step with U.S. soldiers, the size of any residual U.S. force could add fuel to a debate in Washington over whether Taliban-led violence will intensify amid the vacuum left by Western forces, as some U.S. military officials expect.

Military leaders, including U.S. Gen. Joe Dunford, who heads U.S. and NATO forces in Afghanistan, have identified 10,000 soldiers as the minimum needed to help train and advise Afghan forces fighting the insurgency, arguing a smaller force would struggle to protect itself.

During a March visit to Washington, Dunford told lawmakers that without foreign soldiers supporting them, Afghan forces would begin to deteriorate "fairly quickly" in 2015. The Afghan air force, still several years away from being self-sufficient, will require even more assistance, he said.