"Hamid Karzai considers attacking women and children against all accepted international norms and strongly condemns it," the statement said after the airstrike yesterday in Kunar province.
The statement said that according to information from Kunar Provincial Governor Shujaul Mulk Jalala a vehicle "was targeted by a NATO airstrike that killed 16 civilians including women and children".
Earlier the governor had told AFP the dead also included militants.
"Four armed insurgents belonging to al-Qaeda were also killed in the airstrike," he said.
The NATO-led International Security Assistance Force (ISAF) denied that civilians had been killed, saying 10 enemy forces had died in the airstrike.
"We can confirm Coalition Forces' conducted a precision strike yesterday... Resulting in 10 enemy forces killed," ISAF said in a statement.
"At this time, we have no reports of any civilian casualties in regards to this incident," it said.
Civilian casualties in NATO operations have long been a source of friction between the Afghan government and US-led NATO troops, who are winding down operations as they prepare to withdraw by the end of next year.
Kunar, which borders Pakistan, is a stronghold of the Taliban-led insurgency and is also known to have a strong presence of foreign fighters.
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