The NATO strike Wednesday in the province's Zhare District also killed two insurgents, The New York Times reported.
A spokesman for the governor of Kandahar said a NATO aircraft targeted five militants planting mines in the area, killing two and wounding a third. The aircraft then pursued the other two militants.
"The plane chased them, the insurgents entered a street where children were playing and as a result of its shooting, seven people have been killed, including six children, and two girls also have been injured," Zalmai Ayoubi said.
International Security Assistance Force spokesman Master Sgt. Christopher DeWitt said a team was sent to the district to investigate.
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