"We remain committed to our mission in Afghanistan and will continue to work with our Afghan partners to ensure the safety and security of all coalition soldiers and civilians," Army Chief of Staff General Ray Odierno said in a statement.
Maj Gen Greene, the Deputy Commander of the Combined Security Transition Command-Afghanistan, was shot dead at a US army base near Kabul by an individual, whom the Pentagon believes was a member of Afghan National Security Forces.
"Our thoughts and prayers are with Maj. Gen. Harold J. Greene's family, and the families of our soldiers who were injured today in the tragic events that took place in Afghanistan. These soldiers were professionals, committed to the mission. It is their service and sacrifice that define us as an Army," Gen Odierno said.
Greene, 55, was an Army engineer, commissioned in 1980 after graduating from Rensselaer Polytechnic.
Earlier, he had been a top deputy to the Army's acquisitions chief in the Pentagon.
The incident is being jointly investigated by Afghan and ISAF authorities.
In a statement, US Senator Jim Inhofe, ranking member of Senate Armed Services Committee, said the incident is a reminder that despite the steps taken by ISAF, the Afghan National Security Forces and the government of Afghanistan to mitigate insider threats, Afghanistan is still a dangerous place and force protection remains a critical mission.
"As the President withdraws our forces, it is critically important that we listen to our commanders on the ground to determine what is necessary to safely and effectively accomplish our mission in Afghanistan. We owe that to all of the brave service members who have volunteered to go into harm's way in defense of the nation," he said.
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