An Indian police spokesman said on Thursday four rebels were killed in Gool village in southern Udhampur district after police, acting on a tip-off, surrounded their hideout.
He said the militants refused an order to surrender and a firefight ensued, during which four guerrillas were gunned down.
In another incident on Thursday, two militants were killed by members of India's Border Security Force (BSF) in a gunbattle in neighbouring Doda district.
A BSF member was wounded in the clash, he added.
A civilian was killed when suspected militants lobbed a grenade at Indian troops in the Amira Kadal area of Srinagar, which missed its target and killed a watchmaker.
Twelve other civilians were injured in the blast, which sparked panic in the area that was still packed for the Eid al-Fitr holidays, police said.
Police officer killed
Overnight, suspected militants shot dead police officer Shams-u-Din in the central Budgam district. He was working at a police station in Shopian, 50 kilometers south of Srinagar, police said.
In a similar attack, suspected rebels gunned down policeman Reyaz Ahmed at his house. Ahmed worked with the local police counter-insurgency wing in his area of Kulgam, 70 kilometers south of Srinagar.
The Indian and Pakistani militaries on Wednesday began a ceasefire over their border in Kashmir, but both New Delhi and pro-Pakistani rebels have said there will be no truce inside Indian Kashmir, where an insurgency has raged since 1989.