A joint Afghan and NATO investigation team found the civilians died on Thursday when artillery fire failed to hit a target in the Jani Khel district of Paktia Province, the NATO-led International Security Assistance Force (ISAF) said in a statement.
"ISAF officials offer sincere condolences to those affected and accept full responsibility for the actions that led to this tragic incident," the statement, received late on Friday, said.
The country's interior ministry initially blamed the deaths on a rocket fired by insurgents hitting a local bazaar.
Civilian casualties and friendly fire deaths among Afghan security forces have been a frequent irritant between President Hamid Karzai and Western military forces during the nine-year war since the ousting of the Taleban in 2001.
ISAF said commanders had held two days of meetings, or "shuras," with local elders in Jani Khel to discuss the incident.
New US and NATO forces commander General David Petraeus is considering a change to rules of engagement drawn up his predecessor to avoid civilian casualties, following complaints they tie the hands of coalition troops combating insurgents.
Casualties among NATO forces fighting in Afghanistan hit a record high in June and commanders expect violence to rise in parallel with an anti-insurgent offensive in coming months, raising questions about whether more can be done to protect troops.
Two coalition soldiers were killed on Friday in separate bomb attacks, the alliance said, while a suicide car bomb hit a NATO convoy on a bridge outside Jalalabad, killing one civilian and wounding nine others.
Five Afghan government soldiers were accidently killed and two others wounded in a pre-dawn NATO helicopter airstrike on Wednesday, prompting condemnation from the country's government.
The attack took place after a aircraft mistook Afghan National Army soldiers for Taleban insurgents during an operation in southwest Ghazni.
