NATO said they had detained one US soldier over the killings.
Neighbours and relatives of the dead said they had seen a group of US soldiers arrive at their village in Kandahar's Panjwayi district at around 2am (local time), enter homes and open fire.
A senior US defence official in Washington said: "Based on the preliminary information we have this account is flatly wrong. We believe one US service member acted alone, not a group of US soldiers."
An Afghan man who said his children were killed in the shooting spree accused soldiers of later burning the bodies.
The incident, one of the worst of its kind since the US-led invasion of Afghanistan in 2001, quickly inflamed further the severely strained relations between Washington and Kabul.
The US embassy in Kabul said anti-US reprisals were possible following the killings, which come weeks after US soldiers burned copies of the Koran at a NATO base, triggering widespread anti-Western protests in which at least 30 people died.
Afghan President Hamid Karzai condemned the rampage as "intentional murders" and demanded an explanation from the United States. His office said the dead included nine children and three women.
Afghan officials gave varying accounts of the number of shooters involved in the incident. Karzai's office released a statement quoting a villager as saying "American soldiers woke my family up and shot them in the face".
Minister of Border and Tribal Affairs Asadullah Khalid said a US soldier had burst into three homes near his base in the middle of the night, killing a total of 16 people including 11 people in the first house.
A spokesman for NATO's International Security Assistance Force (ISAF) said the US soldier "walked back to the base and turned himself into US Forces this morning", adding there had been no military operations taking place in the area when the incident occurred.
Panjwayi district is about 35km west of the provincial capital Kandahar city. The district is considered the spiritual home of the Taliban and has been a hive of insurgent activity in recent years.
"I saw that all 11 of my relatives were killed, including my children and grandchildren," said a weeping Haji Samad, who said he had left his home a day earlier.
The walls of the house were blood-splattered.
"They (Americans) poured chemicals over their dead bodies and burned them," Samad told Reuters at the scene.
Neighbours said they had awoken to crackling gunfire from American soldiers, whom they described as laughing and drunk.
"They were all drunk and shooting all over the place," said neighbour Agha Lala, who visited one of the homes where killings took place.
"Their (the victims') bodies were riddled with bullets."
A senior US defence official said Defence Secretary Leon Panetta "was deeply saddened to hear last night of this incident and is closely monitoring reports out of Afghanistan". The White House also expressed concern.
The Afghan Taliban said it would take revenge for the deaths, in an e-mailed statement to media.
The US embassy in Kabul said an investigation was under way and that "the individual or individuals responsible for this act will be identified and brought to justice".
The commander of NATO's International Security Assistance Force (ISAF) General John Allen said he was "shocked and saddened" by the shooting, and promised a rapid investigation.
Civilian casualties have been a major source of friction between Karzai's Western-backed government and US-led NATO forces in Afghanistan.
NATO is preparing to hand over all security responsibilities to Afghans by the end of 2014, a process which has already started.
The Koran burning and the violence that followed, including a spate of deadly attacks against US soldiers, underscored the challenges that the West faces as it prepares to withdraw.
All foreign combat troops are scheduled to leave by end-2014.
