The children were killed during a joint Afghan-NATO operation in the Shigal district of restive Kunar province bordering Pakistan late on Saturday.
An Afghan official involved in the operation who did not want to be named said air support was called in after local and coalition forces came under attack, resulting in the death of an American and injuries to several Afghan soldiers.
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 11-year campaign against Taliban insurgents, provoking harsh criticism from Afghan President Hamid Karzai and angry public protests.
The president "strongly condemned the ISAF air strike in Kunar that killed 11 children," in a statement issued by his office.
"The president, while condemning the use of civilians as shields by the Taliban, denounced any kind of operations that cause civilian deaths," the statement said.
Local officials including Shigal district governor Abdul Zahir had earlier given a death toll of 10 children killed and six women wounded, while Sayed Rahman, security commander of Shigal, said one woman was also among the dead.
A spokesman for NATO's International Security Assistance Force (ISAF) confirmed the strike and said the coalition was gathering information to determine what happened.
A US civilian died in a militant attack at the scene, ISAF said.
The interior ministry said in a statement the attack by coalition forces killed six Taliban including two senior commanders.
On Thursday a NATO air strike killed four Afghan policemen and two civilians during a pre-dawn clash with Taliban at a police post in eastern Ghazni province.
After an air strike killed 10 civilians, mostly women and children, in February, Karzai banned Afghan security forces from calling in NATO air strikes.
However it is unclear whether the ban has been enforced and many operations are jointly run by NATO and Afghan forces.
The latest strike came a day after at least five Americans, including a young female diplomat, were killed in two Taliban attacks in the country's east and south.
A suicide car bomber struck a NATO convoy in the southern province of Zabul Saturday, killing three US soldiers and two civilians, one of whom was a female US diplomat.
They were travelling with Afghan officials to distribute books to students. The nationality of the second civilian was unclear.
Another US civilian was killed in an attack in the east, making it the deadliest day for the coalition since July 8 last year.
Though the Taliban have not yet announced their "spring offensive", which started last year with a barrage of bloody attacks in early May, the traditional Afghan fighting season is beginning as the cold winter recedes.
US-led coalition forces are winding down their operations before a scheduled withdrawal of the bulk of their 100,000 troops by the end of 2014, and racing to prepare Afghan forces to take over responsibility for security.
But a brazen attack last Wednesday -- when Taliban gunmen killed 46 people at a court in the western city of Farah to try to free insurgents standing trial -- raised further questions about the Afghans' ability to secure the country.
The Farah death toll was the highest in Afghanistan from a single attack since a Shiite Muslim shrine was bombed in Kabul in December 2011, killing 80 people.