The Taliban claimed responsibility for the bombing inside the heavily fortified Bagram Airfield, north of the capital Kabul, which left 16 other US service members and a Polish soldier wounded as the insurgents ramp up attacks on Western targets.
The dead included two American soldiers and two contractors, in an assault which highlights rising insecurity in Afghanistan nearly two years after US-led NATO forces formally ended their combat operations.
"Force protection is always a top priority for us in Afghanistan, and we will investigate this tragedy to determine any steps we can take to improve it," defense secretary Carter said, adding he was "deeply saddened" by the news.
The blast was caused by a suicide attacker who blew himself up near a dining facility inside the base, said Waheed Sediqi, spokesman for the governor of Parwan province where Bagram is located.
"The attacker was one of the Afghan labourers working there," Sediqi told AFP.
Bagram district governor Abdul Shakoor Quddusi described the explosion around 0100 GMT as "powerful", saying it reverberated across the area. The base was put on lockdown following the attack.
The attack represents a brazen security breach inside one of the most heavily guarded military installations in Afghanistan.
The base is enveloped by multiple layers of Afghan and American guards, security cameras and watch towers, and a surveillance blimp keeps a close watch on the surrounding areas.
"To the family and friends of those who lost their lives today, we share your loss and our thoughts are with you. We offer you our deepest condolences," said John Nicholson, the top US and NATO commander in Afghanistan.
"For the family and friends of those wounded in today's attack, let me assure you they are receiving the best care possible, and we will keep them in our thoughts today."
The militants are stepping up attacks nationwide before the onset of winter, when the fighting usually ebbs.
Bagram Airfield has frequently come under attack by Taliban insurgents.
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