The deaths reopen an often heated debate between those who blame NATO air strikes for civilian deaths and others who argue that NATO air support is vital for protecting vulnerable Afghan security forces.
Afghan police had been patrolling in the southeastern town of Ghazni when they came under attack by insurgents, NATO spokesman Major Adam Wojack said.
"International Security Assistance Forces supported the Afghan unit in contact by engaging the insurgent forces with helicopter-delivered direct fire," he said, adding the coalition was investigating reports of civilian casualties.
Nine Taliban were killed and eight civilians were wounded, said Colonel Mohammad Hussain, a senior police detective.
A Reuters reporter saw the bodies of two children that local people said were killed in the air strike.
Last month Karzai forbade Afghan forces from calling for NATO air support and forbade NATO from striking "in Afghan homes or villages" after Afghan forces called in a strike that killed 10 civilians.
Civilian casualties caused by air strikes are a significant source of friction between Karzai and his international allies as the United States and Afghanistan negotiate over the size of a future American military presence after most international troops depart by the end of 2014.
Some Afghan officials say privately that limiting air strikes exposes the 352,000-strong Afghan security forces to greater danger as they take over the responsibilities of international forces.
Foreign air power is especially critical to cover the mountainous regions near the Pakistani border.