WASHINGTON (CNN) -- A Navy SEAL who was killed in an operation against terrorist group al-Shabaab in Somalia earlier this week has been identified by the Department of Defense as Kyle Milliken, 38, of Falmouth, Maine.

Milliken, a senior chief special warfare operator, was killed Thursday in a remote area of Somalia 40 miles west of Mogadishu when he and other troops came under small-arms fire.

Milliken was a member of SEAL Team Six, a defense official confirmed to CNN. The elite special operations unit, which led the raid that killed Osama bin Laden, was on a scheduled deployment to East Africa for training and carrying out counterterrorism missions. The target in Somalia was a local al-Shabaab leader who had been involved in planning attacks against facilities used by US and African forces in Somalia.

Milliken was on a mission advising Somali National Army forces.

"Senior Chief Kyle Milliken embodied the warrior spirit and toughness infused in our very best Navy SEALs," Rear Adm. Timothy Szymanski, commander of the Naval Special Warfare Command, said in a statement. "We grieve his death, but we celebrate his life and many accomplishments. He is irreplaceable as a husband, father, son, friend and teammate -- and our thoughts and prayers go out to his family and teammates."

Two other military service members were wounded in the operation, including an interpreter who was also a US citizen, a US defense official told CNN.

A US military official confirmed that this is the first US service member killed in action in Somalia since 1993, when two UH-60 Black Hawk helicopters were shot down and 18 American soldiers were killed in the Battle for Mogadishu.

The US troops were part of a US military program to advise and assist Somali ground forces. The mission was not part of the stepped-up effort in Somalia to conduct airstrikes and ground missions against terror targets.