Two militants and as many army men were killed in a fierce encounter at Hajin area of north Kashmir's Bandipora district on Wednesday.
The identity of militants, suspected to be from Pakistan-based Lashkar-a-Taiba, was yet to be ascertained.
"The terrorists opened fire and lobbed a grenade, in which one Garud Commando Corporal Nilesh Kumar Nayan attained martyrdom on the spot while another Garud Commando Sergeant Khairnar Milind Kishor got seriously injured and later succumbed to his injuries", a police spokesman said.
Two Garud squads, each consisting of one officer and 13 other ranks, have been deployed in Kashmir.
The fighting has left tens of thousands dead, majority civilians and earlier this year India launched "Operation Allout" to hunt down the rebels.
Police officials said, one soldier was reported injured in the encounter near Paribal village. Two Kashmiris were also died in a gunfight with Indian security forces in Bandipora district.
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The firing had stopped and search operations were on, local sources said.
The police maintain that almost 25 militants were active in Bandipora district and a group of seven terrorists, led by LeT's Mehmood Bhai, a Pakistani national, is active in Hajin area.
Last week, three rebels and an Indian paramilitary personnel were killed in an attack, when the rebels stormed an army camp outside the airport in Srinagar.
The Army said in a statement that "befitting" tributes were paid to the two IAF martyrs at a wreath-laying ceremony at Srinagar's Badami Bagh cantonment, home of the 15 (Chinar) Corps.
Sources said the team returned the fire in which two terrorists, identified as Nasrullah Mir alias Anna, a local extremist and a foreign terrorist Ali Bai alias Abu Bakker got killed.
According to reports, the operation is still on.
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