"The two Garud personnel were killed in action while operating with the Army for operational experience and training", Defence Ministry spokesman Colonel Rajesh Kalia said.
A jawan was martyred and another is said to be injured in an encounter between terrorists and security forces in North Kashmir's Bandipora district.
It was reported that the gun battle took place between terrorists and security forces in Hajin.
He had recently carried out an attack on a Special Police Officer and his seven-year-old son at Handwara, they had said and added that Khalid was an A++ category top ranking terrorist and carried a cash reward of almost Rs 7 lakh.
The operation was going on till last reports were received.
As the joint team of forces intensified the searches on wee hours, the hiding militants opened fired, triggering a fierce gunfight between the two sides. Two militants believed to be affiliated with Lashkar were also killed in the encounter.
Jammu and Kashmir DGP SP Vaid tweeted, "Encounter in Rakh e Hajin Bandipore".
The soldiers were killed when militants abruptly came out of a house and attacked the party of troopers who were part of CASO, sources said.
The government forces would conduct regular cordon and search operations in the Hajin for a few months now but were expecting to manage contact with the militants as the autumn set in.
The Garud commandos are trained along the lines of Navy's MARCOS and Army's para commandos.