A neighbour said the father had no connection with the Taliban.
Meanwhile, in Kunduz city, the capital of the province, US soldiers detained four Uzbek militants, Afghan authorities said.
The ISAF statement did not name the nationalities of the international forces involved in Thursday's firefight. A spokesman for the German army, which has a base in Kunduz, said German troops were despatched to support the forces that came under fire but the battle had ended by the time they arrived.
In an operation in the southern province of Kandahar on the same day, Afghan and international forces detained six suspected militants in a similar search just west of the provincial capital Kandahar.
The search there targeted militants accused of financing and transporting weapons and supplies for the Taliban in the region, the ISAF said.