The group said it would "take revenge from the invaders and the savage murderers for every single martyr," according to a statement posted on its website, the Times of London reported.
The fear now is that this latest incident could set off a fresh wave of violence.
The attack comes just as outrage stemming from burning of several Korans by members of the U.S. military seemed to be calming down.
The U.S. Embassy in Kabul has warned foreigners to keep a low profile.
Afghan President Hamid Karzai called it "an assassination, one that cannot be forgiven."
The Afghan parliament has passed a resolution in protest of the killings, and asked for a public trial of the U.S. soldier.
U.S. officials were quick to condemn the attack Sunday.
"I offer my profound regret and deepest condolences to the victims and their families," Gen. John Allen, head of NATO forces in Afghanistan, said in a statement.
"This deeply appalling incident in no way represents the values of ISAF [International Security Assistance Force] and coalition troops or the abiding respect we feel for the Afghan people."
NATO has launched its own investigation, and Karzai has sent his delegation to Kandahar for its own inquiry.
The White House said Sunday that Obama called "President Karzai to express his shock and sadness at the reported killing and wounding of Afghan civilians. President Obama extended his condolences to the people of Afghanistan, and made clear his Administration's commitment to establish the facts as quickly as possible and to hold fully accountable anyone responsible. The president reaffirmed our deep respect for the Afghan people and the bonds between our two countries."
ABC News Luis Martinez and Enjoli Francis contributed to this report