The coalition said it was aware of the allegation and was investigating the incident late Saturday in Paktia province.
"We acknowledge that coalition forces were conducting an operation in Paktia province against a large number of insurgents last night and we also are aware of the media reports today of civilian casualty allegations in that area," said Army Lt. Col. Jimmie Cummings, a spokesman for the NATO coalition.
"We are currently looking into this and will release more information as appropriate."
Actions of the Taliban kill more civilians than foreign forces, but the deaths of citizens caught in the crossfire of the decade-long war continue to be an irritant in President Hamid Karzai's relationship with his international partners.
Earlier this month, the Afghan president warned that civilian casualties caused by NATO airstrikes could undermine the strategic partnership agreement he just signed with the U.S.
Rohullah Samon, a spokesman for the governor of Paktia province, said Mohammad Shafi, his wife and their six children died in an airstrike around 8 p.m. in Suri Khail village of Gurda Saria district.
"Shafi was not a Taliban. He was not in any opposition group against the government. He was a villager," Samon said. "Right now, we are working on this case to find out the ages of their children and how many of them are boys and girls."
Any NATO airstrike that leads to civilian deaths erodes the Afghan people's trust in foreign forces.
"If the lives of Afghan people are not safe, the signing of the strategic partnership has no meaning," Karzai's office said earlier this month.
Karzai's warning came after Afghan officials reported that 18 civilians had died recently in four airstrikes in Logar, Kapisa, Badghis and Helmand provinces.
Last year was the deadliest on record for civilians in the Afghan war, with 3,021 killed as insurgents ratcheted up violence with suicide attacks and roadside bombs, the United Nations said in its latest report on civilian deaths. The U.N. attributed 77 percent of the deaths to insurgent attacks and 14 percent to actions by international and Afghan troops. Nine percent of cases were classified as having an unknown cause.
Two civilians died Sunday when their vehicle struck a roadside bomb in Marjah district of Helmand province in the south, said provincial spokesman Daud Ahmadi.
Separately, NATO reported Sunday that four coalition service members had died in roadside bomb attacks in southern Afghanistan.
NATO said in a statement that all four deaths occurred Saturday. It provided no other details on the attacks, including the nationalities of the service members.
One is thought to be a British soldier killed Saturday in an explosion in the Nahr-e Saraj region of southern Helmand province. The British Ministry of Defense announced late Saturday that the soldier died while traveling in a vehicle.
Another NATO service member died Friday in an insurgent attack in eastern Afghanistan.
Their deaths bring to 34 the number of NATO service members killed so far this month in Afghanistan, for a total of 166 this year. A total of 414 members of British forces have died since operations in Afghanistan began more than 10 years ago.
The Afghan Ministry of Interior also announced Sunday that six insurgents were killed Saturday in joint operations in four eastern provinces. Another three were killed when the roadside bombs they were trying to plant detonated in Helmand and Kandahar provinces.