The 38-year-old Bales has not yet been charged. Afghans have called for him to be tried in Afghanistan.
Earlier Friday, Bales' civilian lawyer said his client was likely suffering from stress after witnessing one of his fellow soldiers get his leg blown off a day before Sunday's massacre in Kandahar.
Attorney John Henry Browne says his client was also not happy about being assigned a fourth tour of duty in a war zone. Bales - a married father of two - had served three tours in Iraq where he suffered a head injury and lost part of his foot. The lawyer says Bales was told he would not be deployed to Afghanistan, but that changed "literally overnight."
Bales' family has been moved to a military base near Seattle in the northwestern U.S. for security reasons. Browne told reporters that family members said the staff sergeant never had any animosity towards Muslims and described him as mild-mannered.
U.S. officials have promised a thorough investigation into the incident. Afghan President Hamid Karzai has accused the United States of failing to cooperate with his delegation in the probe.
Karzai met with tribal elders and family members of those killed Friday. He said civilian casualties have been going on "for too long" and that such "behavior can no longer be tolerated."
The Afghan leader also questioned U.S. military insistence that only one shooter was involved in the incident. Villagers say more than one U.S. soldier was involved in the attack in the Panjwai district.
President Karzai met with U.S. Defense Secretary Leon Panetta in Kabul Thursday and demanded that NATO forces pull back from Afghan villages and relocate to their bases in the wake of the shooting spree. Karzai told reporters the demand was also the subject of a telephone conversation with U.S. President Barack Obama Friday.
The White House said the two leaders discussed Karzai's longstanding concerns about coalition night raids - one of the obstacles to the U.S.-Afghan strategic partnership agreement that is being negotiated.
The relationship between the U.S. and Afghanistan has been deteriorating amid various incidents in recent months.