Mahmood Danish, a spokesman for the governor of Kunduz province, told the BBC Taliban fighters had been sheltering in civilian homes.
Nato launched air strikes in the area after two US soldiers were killed.
Mr Danish said it was unclear whether the civilians had died in air strikes or during hand-to-hand fighting.
“All civilian casualty claims will be investigated,” the Nato-led Resolute Support mission said. There were angry protests from civilians, who brought bodies of some of the dead to the governor’s office in Kunduz city, AFP news agency reports.
Images showed the body of an infant girl being carried by a group of civilians.
Taza Gul, a 55-year-old labourer, said: “I am heartbroken. I have lost seven members of my family. I want to know, why these innocent children were killed? Were they Taliban? No, they were innocent children.”
The US military gave no details on the circumstances of its soldiers’ deaths and did not name them.
A further 25 civilians were wounded in the operation in Kunduz, Mr Danish said, and 26 Taliban fighters were killed, including two commanders. The Taliban say only three of their fighters were killed.
The operation took place in an area called Body Kandahari, about 5km (3 miles) from Kunduz city centre, Mr Danish said.
Taliban fighters came close to overrunning Kunduz city last month and the security situation in the area remains febrile. The insurgents control large areas of the province around the city.
The Taliban said US forces had been carrying out a raid to capture three militants when they came under heavy fire.
US combat operations against the Taliban officially ended in 2014 but Special Forces have continued to provide support to Afghan troops.
Afghan forces have suffered thousands of casualties, with more than 5,500 killed in the first eight months of 2016. (BBC) -AT
The Pashtun Times