Petraeus, commander of the NATO-led International Security Assistance Force, said he would personally apologize to Afghan President Hamid Karzai when Karzai returns from London, CNN reported.
Karzai earlier condemned the "ruthless attack," the Los Angeles Times reported. He said all nine victims killed Tuesday were children.
Petraeus said an investigation found that coalition forces accidentally killed the civilians in the Dara-i-Pech district of eastern Kunar province Tuesday. Coalition forces were responding to a rocket attack on their base by insurgents.
The Karzai government and NATO clashed 10 days ago over another incident in Kunar. The Western military said airstrikes killed three dozen rebel fighters, but Afghan officials said more than 60 people died, most of them civilians.
U.S. commanders recently said a string of outposts in the Pech River valley -- previously called vital -- were being abandoned after heavy casualties.
Provincial Police Chief Kahilullah Ziayee said the children, ages 8 to 14, were killed as they gathered firewood for their families to burn in the harsh winter.
Notable deaths of 2014 [PHOTOS]