Security forces launched a cordon and search operation in Hajin area of Bandipora district in the early hours today following information about the presence of militants in the area, an Army official said.
He said the militants opened fire on the security forces, triggering a gun battle.
Two IAF Garud personnel, who were part of the operation for training and experience purpose, were injured in the exchange of fire with the militants, the official said.
The injured personnel were evacuated to 92 Base Hospital here where they succumbed to injuries.
They have been identified as Sergeant Milind Kishor and Corporal Nilesh Kumar.
Two militants have been killed in the encounter, the official said adding the slain ultras belonged to Lashkar-e- Toiba (LeT).
They have been identified as Ali alias Abu Maaz, a Pakistani militant, and Nasrullah Mir, a local militant.
Director General of Police (DGP) S P Vaid said these militants were involved in a number of terror attacks in which security forces personnel and civilians were killed.
"It is a big success for security forces," Vaid said.
A police official said two AK rifles, one pistol, one hand grenade 12 AK magazines and 75 rounds were recovered from the scene of the encounter.
"Chinar Corps Commander and all ranks salute the supreme sacrifice of India Air Force Garud martyrs of Hajin operation," an Army official said.
A wreath-laying ceremony was held at Badamibagh headquarters of the Army here for the soldiers.
Senior officers from the Army, police and IAF were present at the ceremony.