The soldier was playing with a group of children outside when the attacker came from behind and stabbed him in the neck with a large knife, Khan said, adding the young man had escaped to nearby Pakistan.
Taliban spokesman Zabiullah Mujahid said the young man was acting independently when he killed the soldier but had joined the Islamic militant movement since fleeing the scene.
The Pentagon said in a statement last week that Cable, of Philpot, Ky., died from injuries sustained when his unit was attacked by enemy forces.
At least 14 U.S. soldiers died in March, compared with four in the previous two months, according to an Associated Press tally.
The number of American troops killed in Afghanistan has dropped sharply as international forces increasingly take a back seat while preparing to end their combat mission by the end of 2014. But they continue to face dangers ranging from roadside bombs to attacks by their Afghan counterparts or insurgents disguised as government forces.