The Army identified the slain militant as Shahid Ahmed Dar, a resident of Shopian's Jamnagri village.
Also on Monday, a top militant of another Pakistan-based militant group Jaish-e-Mohammad (JeM) was killed during a gunfight in south Kashmir's Pulwama district, police said.
Four civilians and a terrorist were killed in army action after terrorists reportedly attacked an army check point at Pohnoo village of Shopian, though army claimed that they killed a terrorists and four over ground workers, a claim rejected by locals. "In the retaliatory fire, one militant was killed and a weapon has been found with him", Kalia said.
Three others were found dead in a vehicle some distance away.
The locals alleged that the civilians were travelling in a auto through the area and were killed in reprisal by the Army following the militant attack.
"Varying accounts from the Chief Minister and the Security Forces on the incident are unfortunate and further perpetuate the sense of disenchantment, distrust and alienation", he said.
The various business communities of the valley also reacted to the killings. The Indian army described them as accomplices but police were investigating this claim.More news: N gains control of Senate, say media
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The Police have reached the spot and begun legal formalities.
They were stopped and taken into preventive custody, the officials said.
She tweeted: "Deeply distressed by more deaths of civilians caught in the crossfire in Shopian".
Schools and other education institutes, which were to open on Monday after a two-month winter break, remained closed as a precautionary measure in the Valley.
In occupied Kashmir, complete shutdown will be observed, tomorrow, against the civilian killings in Shopian and shifting of illegally detained Hurriyat leaders from Srinagar central jail to jails in Jammu.
The body of Gowhar Ahmad Lone, 24, of Molu Chitragam, Shopian, was found around 250 meters away from the site at Pahnoo.
Police intercepted the Malik-led protest march and took the separatist leader and some of his supporters into custody.
Indian security forces beefed up their presence across the region and officials blocked internet service in south Kashmir to maintain law and order, officials said.