Relations between Washington and Kabul have been rocky for years, and negotiations over an agreement that would allow some US troops to remain in the country after this year have broken down into a long-running public dispute.
"As a result of bombardment by American forces last night... In Siahgird district of Parwan province, one woman and seven children were martyred and one civilian injured," a statement from Karzai's office said.
Civilian casualties have been one of the most sensitive issues of the 13-year military intervention in Afghanistan, and Karzai has often used accidental shootings and misguided airstrikes to berate foreign countries and stir public anger.
NATO's International Security Assistance Force (ISAF), earlier said it was "aware of reports that at least two civilians were inadvertently killed today during an Afghan-led joint operation in Ghorband (Siahgird) District".
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ISAF added that one of its soldiers was killed in the fighting, as well as at least 10 insurgents.
A Taliban spokesman said that 12 Afghan soldiers had been killed, but the insurgents often exaggerate death tolls.
Siahgird district, about 40 kilometres north of Kabul, is on the main road from the capital to Bamiyan.
The route was considered safe, but the region has become increasingly violent with major clashes between Afghan security forces and the Taliban erupting since October.