The attack on the relatively new outpost began at 4:30 a.m. Sunday and lasted throughout the day.
Nine U.S. troops were killed in the attack, a Western official said on condition of anonymity because the deaths had not yet been officially announced.
Lt. Col. Rumi Nielson-Green, the top U.S. military spokeswoman in Afghanistan, said she could not comment because the battle was ongoing. She referred calls to NATO headquarters in Kabul.
NATO said in a statement that there have been casualties on both sides but accurate numbers could not be confirmed because the fighting was ongoing.
The attack appeared to be the deadliest for U.S. troops in Afghanistan since June 2005, when 16 American troops died were killed -- also in Kunar province -- when their helicopter was shot down by a rocket-propelled grenade.
Those troops were on their way to rescue a four-man team of Navy SEALs caught in a militant ambush. Three SEALs were killed, the fourth was rescued days later by a farmer.