"Hamid Karzai considers attacking women and children against all accepted international norms and strongly condemns it," the president's office said in a statement released Sunday.
NATO announced the deaths of 10 fighters in the strike, but did not report civilian casualties.
Afghan officials said at least nine civilians were killed in the airstrike and while a provincial police chief said 16 civilians died, including four women and four children.
Kunar province police chief Abdul Habib Sayed Khaili said a drone struck hit a pickup truck carrying women and children after three Arab and three Afghan fighters came on board in Qoro village.
According to the United Nations, about 1,000 Afghan civilians have been killed and another 2,000 wounded in the first half of 2013, up 24 percent from the same time last year.