Kabul, Afghanistan (CNN)
-- An American soldier left his base in Afghanistan and went from house to house in two villages, killing 16 people in their homes, a provincial official told CNN Sunday.
NATO's International Security Assistance Force confirmed that a soldier had gone off base and fired on civilians before turning himself in, but did not say how many victims there had been.
There has been confusion about the number of casualties since the shooting in Kandahar province, eastern Afghanistan, with different sources offering different numbers.
Regardless of the number of victims, the incident looks likely to inflame tensions still further between foreign troops and Afghan civilians, many of whom were enraged by the burning of Qurans by American troops last month.
American officials from President Barack Obama down called the burning an accident and apologized for it, but riots left dozens dead, including four American troops. Hundreds more were wounded.
On Sunday, ISAF's deputy commander, Lt. Gen. Adrian Bradshaw, expressed "deep regrets and sorrow at this appalling incident."
"One of our soldiers is reported to have killed and injured a number of civilians in villages adjacent to his base," Bradshaw said in a statement.
Capt. Justin Brockhoff of ISAF said there had been "multiple" casualties and that the injured Afghans were being treated in ISAF facilities.
The U.S. Embassy in Kabul said it deplored "any attack by a member of the U.S. Armed Forces against innocent civilians," and assured "the people of Afghanistan that the individual or individuals responsible for this act will be identified & brought to justice."
A provincial council member, Ahsan Noorzai, said earlier that 18 people were killed, but did not say where his information came from.
The Taliban claimed that 50 people had been killed, but the Islamist militia regularly exaggerates casualty figures.
They disputed ISAF's version of events, saying several soldiers went on a raid that resulted in dozens of deaths.
But Maj. Jason Waggoner, another ISAF spokesman, said: "The civilian casualties were not the result of any operations. The soldier was acting on his own. After the incident he returned to the compound and turned himself in."
Brockhoff said officials do not yet have a motive for the shooting, which is under investigation by both NATO and Afghan officials.
"This is a deeply regrettable incident and we extend our thoughts and concerns to the families involved," a statement from ISAF said.
Civilian casualties as a result of action by the NATO-led international coalition have long caused anger in Afghanistan, adding pressure on international forces to withdraw.
The international force has said avoiding civilian casualties is a high priority.
"My command's mission is to protect the civilian people of Afghanistan," Gen. John R. Allen, ISAF commander, said last month. "I take very seriously the loss of every Afghan life. We will continue to do all we can to ensure the safety of the Afghan population."
The number of ISAF-caused civilian deaths decreased by nearly 17% from 2010 to 2011, the coalition force said in its December monthly report.