The US soldier died when an Afghan army fighter yesterday opened fire on an American delegation outside the governor's compound in Jalalabad, the capital of the militant-infested province of Nangarhar.
"I don't know all the circumstances of that incident, yet it's possible it's a 'green on blue' incident of the kind we've had before," Carter said, referring to insider attacks by Afghan troops on their NATO partners.
"The main thing obviously on my mind is the service members and their families. It's a reminder Afghanistan is still a dangerous place," he said shortly before leaving Tokyo for Seoul.
Yesterday's incident was the first such attack since Washington announced a delay in troop withdrawals from Afghanistan, responding to a request from Afghan President Ashraf Ghani.
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Most NATO combat troops withdrew from Afghanistan last year but a small contingent remains, including about 10,000 US forces.
The US Army soldier was part of a unit devoted to training and advising Afghan forces, officials told AFP.
US troops returned fire, killing the gunman and wounding two other Afghan soldiers, local police said.