Afghan President Hamid Karzai (Creative Commons)

The deadly incident, which occurred in Kandahar's Panjwayi district, could trigger further tensions between foreign troops and Afghan civilians, many of whom were angered by the burning of Qurans by American forces last month. President Barack Obama's administration has apologized for the book burnings, but riots during the aftermath left dozens dead.

"The murdering of innocent people intentionally by an American soldier is an act of terror that is unforgivable," Afghan President Hamid Karzai said.

NATO confirmed that a soldier had gone off base and fired on civilians before turning himself in, according to CNN. But the Taliban disputed NATO's version of the events, claiming that several soldiers went on a raid that led to as many as 50 deaths.

Neighbors said they awoke to gunfire from American soldiers, whom they described as laughing and drunk, Reuters reported.

"They were all drunk and shooting all over the place," said neighbor Agha Lala, who visited one of the homes where the incident took place. "Their bodies were riddled with bullets."

A U.S. defense official in Washington rejected those witness accounts, stating that one service member acted alone in the shootings.

U.S. Air Force Captain Justin Brockhoff, a coalition spokesman in Kabul, said a joint Afghan-coalition investigation was underway. Brockhoff said it wasn't clear what the shooter's motive was, and whether he has had previous contact with the victims, the Wall Street Journal reported.

"Every effort will be made to establish the facts and to hold anyone responsible to account," British Army Lt. Adrian Bradshaw, the coalition's deputy commander, said in a statement.

The shooting was not the first incident of its kind in Kandahar. Last year, four U.S. soldiers were convicted of murdering Afghan civilians for sport and collecting their body parts as trophies in 2010.