The children were killed during a joint Afghan-NATO operation in the Shigal district of restive Kunar province bordering Pakistan late on Saturday.
"Ten children and eight militants were killed in the strike, six women were wounded," Wasifullah Wasifi, the spokesman for Kunar province, told AFP.
Shigal district governor Abdul Zahir confirmed the death toll and said people had brought the children's bodies to the centre of the town. The wounded women were taken to Kunar's central hospital, he said.
An Afghan official involved in the operation who declined to be named said the air support was called in after local and coalition forces came under attack, resulting in the death of an American and injuries to several Afghans.
The official said the force did not know there were women and children in the houses that were hit.
Civilian casualties caused by NATO forces have been one of the most contentious issues in the campaign against Taliban insurgents, provoking harsh criticism from President Hamid Karzai and angry public protests.
Sayed Rahman, security commander of Shigal, said one women was also among the dead. "We have reports that 10 children and one woman have been killed in the air strike," he said.
A spokesman for NATO's International Security Assistance Force (ISAF) confirmed the strike, but said up to 10 women and children were wounded in the attack rather than killed.
A US civilian died in a militant attack at the spot, he said.
The interior ministry said in a statement the attack by coalition forces killed six Taliban including two senior commanders.
A NATO air strike on Thursday killed four Afghan police and two civilians in Ghazni province.
That attack happened after Taliban insurgents raided a local police post before dawn and NATO planes were called in to support the officers.