Several hundred villagers in Nangarhar Province took to the streets blaming US-led troops for the deaths.
A local official said it was not clear who killed them. The coalition said it could not confirm any civilian deaths.
US-led forces say they have killed 55 militants in clashes further south. There is no independent confirmation.
A statement said 25 other "anti-Afghan forces" had been injured and three detained after coalition troops were ambushed in Paktika province on Friday.
Meanwhile, Afghan intelligence officials say they have foiled a potential bombing after recovering a pressure cooker packed with explosives in the capital, Kabul.
'Death to America'
Protesters demonstrated in Khogyani district of Nangarhar province on Monday.
A BBC reporter in the nearby city of Jalalabad said 200-300 people took part.
They shouted "death to America" and called for foreigners to leave the area as well as for compensation to be paid after the deaths of the civilians.
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Khogyani district governor Zalmi Khan told the BBC: ''A joint Afghan-American convoy was ambushed by the Taleban. Security forces returned fire and killed one Taleban - three others fled.
"The dead body of the Taleban and his weapons are lying there.
"As a result of the firing, one child and father got killed. We don't know whose firing killed them.''
The BBC's Bilal Sarwary in Kabul says Khogyani district is a remote and mountainous area on the border with Pakistan.
He says there have been demonstrations against foreign forces there in the past when poppies were eradicated.
Civilian deaths at the hands of foreign forces have prompted a number of protests in Afghanistan. President Karzai has repeatedly urged international troops to be more careful.
Last year US forces said they were deeply ashamed" by the killings of 19 Afghan civilians by US Marines in Nangarhar Province.
Correspondents say many more civilians are killed in attacks and suicide bombings by insurgents opposed to the Western-backed government in Kabul.
© 2008 BBC News