"The fighting erupted on Monday and continued Tuesday," an Indian police officer, who wished to remain anonymous, told AFP.
"So far three militants, two policemen and an army officer have been killed," the officer said, adding the gunfight erupted in northern Kashmir`s Kupwara district when police and army raided a militant hideout.
Kupwara borders Pakistan-administered Kashmir.
The Himalayan region is divided between nuclear-armed India and Pakistan, but claimed by both nations.
The dispute has triggered two of the three wars fought by the neighbours since independence from British colonial rule in 1947.
According to an official count, 47,000 people have died in Kashmir in more than two decades of rebellion against New Delhi`s rule. (*)