The Taliban described the attack as a 'heroic operation' in a message on their official Telegram channel
One American service member was killed and two others were wounded on Saturday in what the U.S.-led coalition described as an "apparent insider attack."
"The wounded service members, who are in stable condition, are currently being treated," said a statement by the NATO Resolute Support Mission. "The incident is under investigation."
Details of the attack were scant.
The Taliban did not claim responsibility for the attack, but acknowledged it in a message on its official Telegram channel. The attack took place at Tarinkot Airport in the the southern province of Uruzgan and was carried out by a member of the Afghan security forces, it said.
It was not immediately clear what became of the shooter.
The coalition said the deceased would not be identiied publicly for 24 hours in order to give officials time to notify next of kin.
The Taliban have been battling U.S.-led NATO forces in an attempt to restore their version of strict Islamic law in the country after being toppled by a U.S.-led campaign in 2001. Efforts to impose a ceasefire in the region have been mostly unsuccessful.
Last year, the United States added thousands of additional troops to its forces in Afghanistan, which are engaged in both training and advising Afghan forces and conducting counterterrorist missions against Islamic State and other militant groups.
As in other areas of the war, Afghan units suffer more heavily than coalition units from insider attacks. A Pentagon report last month said there were 47 so-called "green-on-green" attacks, or incidents where Afghan soldiers turn on their own side, so far this year.