Six of the militants were killed in the village of Kumhar Mohalla, in the northern Kashmir district of Kupwara, an army spokesman said.
"Two of the slain militants have been identified as divisional commanders of Lashkar-e-Taiba," the spokesman said, referring to a hardline rebel group responsible for most of the suicide attacks in Indian Kashmir.
One of the other slain rebels was a Lashkar operative and the other three belonged to another hardline group, Harkat-ul-Jehadi Islami, the spokesman said.
The six were killed in an encounter during a "cordon and search" operation by the Indian army's Kilo Force - a counter-insurgency wing operating in northern Kashmir.
Another two rebels were killed by the army in two separate encounters in northern Baramulla district and in Poonch in southern Kashmir, the spokesman said.
Rush for passports
Meanwhile, with Kashmir's border areas no longer rocked by artillery fire, Kashmiris are thronging for passports so they can visit relatives caught in the no-go zones for more than 50 years.
Scores of people turn up at the local passport office every day in Jammu, Indian Kashmir's winter capital, in search of the documents that will allow the long-overdue family reunions, officials say.
"Most applicants want to travel to Pakistan," passport officer
Madan Lal said.
One of those in the queue, Gulzar Ahmed, had travelled to Jammu from the Rajouri border area to apply for passports for his entire family.
"Passport applications have been received from government officials and those working in police and paramilitary forces keen to visit their relations in the western countries. But the main rush has been from Muslims wanting to travel to Pakistan and (Pakistan-administered) Kashmir"
"We want to travel to Mirpur in Pakistan where my uncle and other relations have been living since 1947," Ahmed said.
The trip has become feasible since India and Pakistan eased travel restrictions and announced on November 26 a ceasefire along their disputed borders.
Since last July a bus has been operating between Delhi and Lahore across the main Wagah border post while air and train links were re-established early this month.
But Ahmed is waiting for a direct bus service to be established between the Indian and Pakistani zones of disputed Kashmir, a move which India has mooted.
Once the bus service is up and going, Ahmed and his family will be first in the queue - passports in hand.
"We will have easy travel mode available and for this a passport is a must," Ahmed said.
Already 1400 people had applied for passports in the first three weeks of January alone, Lal said.
Many applications had been received from people living in the border areas of Poonch and Rajouri.
"Applications have been received from state and Indian government officials and those working in police and paramilitary forces keen to visit their relations in the western countries but the main rush has been from Muslims wanting to travel to Pakistan and (Pakistan-administered) Kashmir," Lal added.