The soldier was flown from Afghanistan to Kuwait on Wednesday, setting off more protests that the soldier be tried in Afghanistan. The Pentagon has said the U.S. doesn't have appropriate detention facilities in Afghanistan, but U.S. officials say a trial in Afghanistan is still possible.
The controversy comes as U.S. Secretary of Defense Leon Panetta met with Afghan President Hamid Karzai. The meeting was scheduled before the killings.
Karzai on Thursday demanded that NATO troops immediately pull out of rural areas and called for Afghan troops to take the lead for countrywide security by 2013, a year ahead of the current target date.
Karzai told Panetta that Sunday's shootings in southern Afghanistan were cruel. He said everything must be done to prevent similar incidents in the future, so the international forces should speed up their transfer of authority to Afghan troops.
President Barack Obama and British Prime Minister David Cameron said in Washington on Wednesday that they and their NATO allies were committed to shifting to a support role in Afghanistan in 2013. But Obama said the overall plan to gradually withdraw forces and hand over security in Afghanistan will stand.
The Associated Press contributed to this report.