"I want to express my shock and sadness at the tragic shooting incident in Kandahar province, where it is reported that several people, including women and children, have been killed or wounded," he said in a statement.
"I offer my heartfelt condolences and sympathy to their families and loved ones, and to the Afghan people and government," he added.
The alliance`s secretary general gave his full backing to the investigation launched by General John Allen, commander of the US-led International Security Assistance Force there.
"We remain firmly committed to our mission of building a strong and stable Afghanistan, together with our Afghan partners," Rasmussen added.
According to a statement earlier from Afghan President Hamid Karzai, the American soldier entered the homes of civilians in southern Kandahar province and killed 16 people including nine children and three women.
Condemning the slaughter as "unforgivable", Karzai has demanded an explanation from the US government.
The US embassy in Kabul has sent out an alert to its citizens in Afghanistan warning that as a result of the shooting "there is a risk of anti-American feelings and protests in coming days".
Kandahar is a stronghold of Taliban insurgents fighting to oust Karzai`s government, which is supported by some 130,000 US-led NATO troops. (*)
Editor: Kunto Wibisono
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