US President Barack Obama has promised that international forces will not "rush for the exits" in Afghanistan.
Mr Obama said foreign troops must be withdrawn in a responsible way.
The killings in Kandahar province have strained relations between Afghans and foreign forces.
US Defence Secretary Leon Panetta says the suspect could face the death penalty, if found guilty.
Mr Panetta said that the intention was to try the case in a US military court.
Asked whether the soldier, who gave himself up, had confessed to the alleged crimes, the US defence secretary said: "I suspect that that was the case."
On Tuesday morning, some 600 students took part in a rally in the eastern city of Jalalabad, condemning the attack and chanting "Death to America! Death to Obama!".
The Taliban has renewed threats of revenge attacks, saying it would behead "sadistic（虐待狂的） " American soldiers.
Mr Obama told local CBS station KDKA on Monday that the shooting was "absolutely heartbreaking and tragic".
When asked if the incident had made him think that the troop withdrawal should be quickened up, he said: "It makes me more determined to make sure we're getting our troops home."
He added: "What we don't want to do is to do it in a way that is just a rush for the exits."
Mr Obama said that international forces had to make sure the Afghans could secure their borders and stop al-Qaeda from getting back into the country.
Afghan MPs passed a motion earlier saying Afghans had run out of patience.
Anti-US sentiment is already high after soldiers burned some copies of the Koran at a Nato base in Kabul last month, sparking deadly riots across the country.
Senior aides close to Afghan President Hamid Karzai told the BBC: ''We want the soldier to be tried at a US court under US law - but in the presence of media, in a transparent manner, at a speedy trial which could be satisfactory for the victims, the people of Kandahar and Afghanistan."
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