The commander of NATO forces in Afghanistan, General John Allen, has apologised for the killings in Logar province during a joint operation with Afghan forces on Wednesday and promised an investigation into circumstances leading to the air strike.
Karzai met Allen and U.S. ambassador Ryan Crocker on Saturday and said that such strikes were a violation of a strategic partnership agreement between the two countries last month both in "text and spirit", the president's office said a statement late on Saturday.
"NATO commander once again officially apologised about the civilian casualties in Baraki Barak district of Logar and agreed with President Karzai. He gave a commitment that his forces will not launch air strikes in residential areas," it said.
NATO initially said its forces and Afghan troops came under fire during the operation to capture a Taliban commander and they called for an air strike.
It said operational reports indicated that two women received non-life threatening injuries and that a number of insurgents were killed.
Later, as villagers displayed bodies of women and children from the ruins of two houses, the NATO-led force said it had ordered an investigation. Nine of the victims were children, including an infant, five were women and three were elderly people, police said.
Karzai's chief spokesman, Aimal Faizi, said the air strike was ordered unilaterally without coordinating with the Afghan forces on the ground.
Afghan forces had surrounded the compound and if there was firing coming from inside they could have dealt with it, he said. "A few minutes of patience would have saved the lives of civilians."
The U.S.-led NATO force, preparing to hand over security responsibilities to Afghan forces by 2014, has stepped up operations against the Taliban in the south and east of the country.
But the deaths of civilians in some of these operations has fuelled resentment against foreign forces and become a rallying cause for the Taliban fighting to throw them out of the country.
"If the bombings on Afghan homes continue, they will be regarded as a violation and an act of aggression," Faizi said.