Abdul Wali, the deputy governor of Paktia province, said the strike killed seven civilians including a nine-year-old child.
But NATO has denied the claims, saying the strike killed eight militants who had fired on its forces.
Locals say they were gathering firewood on a mountain side when NATO forces fired on them.
"They had shovels in their hands, and coalition forces maybe thought they were insurgents," Mr Wali told Reuters.
“The Afghan nation is tired of such killings. We are going to seriously investigate this incident and we strongly condemn such a killing and whoever committed this crime must be held accountable for their action."
But Lt. Col. David Olson, a spokesman for the US-led military coalition, disputes reports of civilian deaths and said that a precision airstrike had taken place in the area after NATO forces came under fire.
"The result of this strike was eight enemy killed," he said.
Both the Taliban insurgency and the militant Haqqani network are active in Paktia province.
The United Nations estimated that air strikes accounted for 1 per cent of the nearly 5,000 deaths and injuries of civilians in the first half of 2014.
Civilian casualties were one of the reasons that former President Hamid Karzai cited for refusing to sign a bilateral security agreement with the United States to allow a small US force to stay after the end of this year.
Mr Karzai's successor, President Ashraf Ghani, signed the security deal the day after taking office.
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