At least one woman was reportedly killed and a further six are believed to have been injured in the incident in Shigal district, Kunar province.
Nato confirmed that "fire support" was used in Shigal after a US civilian adviser died in a militant attack, but said it had no reports of deaths.
Afghan President Hamid Karzai condemned the killings.
A statement issued by his office said he had already issued a decree banning aerial attacks on civilian areas.
Villagers and officials told the BBC that the casualties were inside their homes when they died.
Photographs apparently sent from the scene to international news agencies appeared to show the bodies of several dead young children, surrounded by Afghan villagers.
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.
The narrow and mountainous valley of Shultan lies 30km (20 miles) away from the provincial capital of Asadabad, right on the border with Pakistan's Bajaur tribal agency.
The area is covered with dense forest, offering the perfect cover for insurgents.
Afghan intelligence officials in Kunar say Afghan and foreign fighters have a big presence in the area and often launch attacks against Afghan and international forces in Afghanistan, and against Pakistani military positions across the border.
The area has been the site of intense fighting between Taliban and US/Afghan forces for the last 10 years, with US-led forces often carrying out operations in the valley targeting Afghan Taliban and foreign fighters with al-Qaeda backing.
The Afghan government has struggled to exert its control in this strategic district despite several major American offensives, as the militants keep re-grouping.
Afghan counter-terrorism officials in the province say foreign fighters have been training local fighters in the area for quite some time, and their presence has become a major threat for the security of Kunar province.
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."
A statement issued on behalf of President Karzai strongly condemned the Nato attack, and "military operations in residential areas that cause civilian deaths".
"The president also strongly condemns the Taliban's tactic of using civilians and their homes as their shields," it said.
International forces are preparing to withdraw from Afghanistan by the end of 2014. Civilian deaths in Western military operations have been a source of tension between the Afghan government led President Karzai and the US and its Nato allies.
In February last year, at least 10 civilians, mostly women and children, were killed in a Nato air strike in the same area.
In February this year, President Karzai ordered a complete ban on Afghan security forces calling in air strikes in residential areas.
As if this war wasn't enough of a screw up to begin with.
I was thinking that the war in Afghanistan had ended, but that's only because we pulled out early. So it wasn't our fault (y). Black humour aside, I don't think it's too terrible. From our perspective and not the Afghans because we're transitioning out of Afghanistan in a year or two anyways. So soon enough there will be no more occupation and atrocities like these will become a memory.