A wave of Taliban suicide bombers backed by gunmen attempted to breach the defences of the main United States base for southeastern Afghanistan on Monday night.
NATO troops were still fighting the remaining Taliban insurgents after they were driven back to some houses in a nearby village, the provincial governor said.
The Afghan Defence Ministry said 13 suicide bombers were killed.
On Monday, a suicide bomber killed 10 Afghan civilians and wounded 13 more outside the same base.
The attacks on Camp Salerno, close to the Pakistan border, are the most brazen on a big foreign base for some time and point to a greater confidence among Taliban militants who have stepped up their insurgency this year.
A group of 30 Taliban fighters, among them six suicide bombers, attacked the camp, close to the town of Khost, provincial governor Arsala Jamal said.
"Since then, there has been a clash going on between NATO and the Taliban. Six Taliban were killed after they blew up the bombs they had on their bodies. Two children have been killed and two more, along with a woman, have been wounded," he said.
NATO troops pushed backed the Taliban attack with air support.