The statement said that the strike in the southern province of Helmand was carried out Saturday after insurgents who had earlier killed a patrolling marine hid in a compound and carried on firing.
The compound hit by the air strike was home to civilians. Local officials said that five girls, seven boys and two women were among those killed by international forces.
"I want to offer my sincere apologies for the nine civilians who were killed during the incident in Now Zad District, Helmand province, that occurred on 28 May," said a statement from Major General John Toolan, International Security Assistance Force (ISAF) commander for the southwest region of Afghanistan.
He stressed it was the coalition's "top priority" to avoid civilian casualties, adding that a full investigation was under way.
"While I know there is no price on human life, we will ensure that we make amends with the families in accordance with Afghan culture," Toolan added.
The apology came after Karzai's office issued what it said was a "last warning" to US and NATO-led troops over civilian casualties following Saturday's incident, which it described as a "great mistake." In response, White House spokesman Jay Carney said "we share and take very seriously" Karzai's concerns.
Civilian deaths in international military operations are a highly sensitive topic in Afghanistan, frequently sparking angry demonstrations and vocal condemnations from Karzai. The United Nations says Afghan civilian deaths in the war increased 15 per cent to a record high of 2,777 last year.