Details of the shooting incident remained unclear, said the official, who spoke on condition of anonymity. The victims were employed under a US Defense Department contract and died from gunshot wounds.
Western troops and civilians training Afghan security forces have faced lethal assaults from Afghans in uniform who turn their guns on their counterparts.
Nato troops have adopted special security measures in recent years to try to counter the threat.
The airport in the Afghan capital Kabul is heavily guarded, with one section devoted to commercial aircraft and another area set aside for a Nato contingent.
Thursday's attack came after a surge in violence by the Taliban insurgency over the past year.
"Ghazi Ehsanullah succeeded last night to achieve the target and used his gun to hit a group of the US soldiers," the Taliban spokesperson said.
At least nine people were killed earlier Thursday in the country's east when a suicide bomber detonated an explosive at a funeral for victims of a roadside bomb attack.
Most Nato combat troops pulled out of Afghanistan last year but a small contingent of about 12,000 remains in the country, including roughly 10,600 American forces.
The American soldiers, along with other Nato troops and private contractors, are helping the Afghans improve their logistics and build up a fledgling air force.
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"Insider attack ? " MAy be .. pehaps ... I am sure you will now find some way to some how link this to your fav whipping boy - India.