A further six women are believed to have been injured in the incident in Shigal district, Kunar province.
Villagers and officials told the BBC that the casualties were inside their homes when they died.
Nato confirmed that “fire support” was used in Shigal but said it did not have any reports of civilian deaths.
A local official said eight Taliban insurgents had also died in the air strike on Saturday, which is reported to have caused the roofs of several houses in three villages to collapse.
He said the strikes were called in to support a major operation by US and Afghan government forces targeting senior Taliban commanders and a local weapons cache.
Tribal elder Haji Malika Jan told the BBC: “The fighting started yesterday morning [Saturday] and continued for at least seven hours. There were heavy exchanges between both sides.
“The area is very close to the Pakistani border and there are hundreds of local and foreign fighters, mostly Pakistanis, in the area.”
In a statement, the Nato-led International Security Assistant Force (Isaf) said: “We are aware of an incident yesterday in Kunar province in which insurgents engaged an Afghan and coalition force.
“No Isaf personnel were involved on the ground, but Isaf provided fire support from the air, killing several insurgents. We are also aware of reports of several civilians injured from the engagement, but no reports of civilian deaths. Isaf takes all reports of civilian casualties seriously, and we are currently assessing the incident.
“The air support was called in by coalition forces – not Afghans – and was used to engage insurgent forces in areas away from structures, according to our reporting.”
International forces are preparing to withdraw from Afghanistan by the end of 2014. Civilian deaths in Western military operations have been a source of friction between the Afghan government led by Hamid Karzai and the US and its Nato allies.