The incident occurred overnight in a village in Nadir Shah Kot district in the province of Khost, around 220 kilometres from the capital Kabul. (Agencies)
Khost provincial spokesman Mubarez Mohammad Zadran said, "The woman and her two sons aged 10 and nine were killed after they had erected a tent on a mountain in Zanikhail village of Nadershah Kot district."
Villagers in the area sometimes take their animals to graze in the countryside and spend the night in tents when far from home.
Karzai called the strike a violation of agreements between the two countries and strongly condemned it, according to a statement by his office.
According to Zadran, the strike could have been a case of mistaken identity.
"Initial information we have show that the air strike by foreign forces' helicopters may not have been deliberate," he said.
He added that Afghan National Army and foreign forces conduct operations in the area against members of the Haqqani network.
A spokesman for the International Security Assistance Force said: "ISAF takes all allegations of civilian casualties seriously. We are looking into these allegations and will provide more information as available."
Civilian casualties in NATO operations have long been a source of friction between the Afghan government and US-led NATO troops, who are winding down operations as they prepare to withdraw by the end the year.
The strike came as officials count votes from the April 5 election to choose a successor to President Hamid Karzai.
Early results suggest former foreign minister Abdullah Abdullah, runner up in the 2009 presidential poll, is leading his closest rival Ashraf Ghani, but a run-off is likely.
The incident occurred overnight in a village in Nadir Shah Kot district in the province of Khost, around 220 kilometres from the capital Kabul.