A spokesman for the governor in Nangahar province said an Afghan commando had opened fire on the US troops during a joint operation in Achin. He was shot dead in return fire.
Another US soldier was reportedly wounded in the attack.
A spokesman for the Taliban said it had carried out the attack.
Islamic State militants also operate in the area.
Earlier, at least two Afghan policemen were killed by US forces in a so-called friendly fire incident in southern Afghanistan.
