Police Inspector-General Muneer Ahmed Khan said three militants, a term used by Indian authorities to refer to separatist fighters in Kashmir, were killed early on Wednesday after clashes with security forces at residential neighborhood west of the capital Srinagar.
The official said Indian troops started the shooting overnight after receiving tips about a hideout in Radbugh. He said the fight lasted for hours.
Authorities on Wednesday imposed restrictions in old city following the clashes with reports indicating that Hizb ul Mujahideen fighter Sajad Ahmad Gilkar, who belonged to Pandan locality in Nowhatta area, was among the three who in clashes with security forces.
Authorities have also suspended Internet services on mobile phones in Srinagar and Budgam as a "precautionary measure".
India and Pakistan have fought three wars since their independence in 1947, two of them over the Muslim-majority Himalayan region of Kashmir which they both claim in full but rule in part.
The conflict in Indian-controlled Kashmir is basically a struggle for self-determination with residents of the region demanding a plebiscite while India rejects the call.
The partition of British colonial India into the dominion states of India and Pakistan in 1947 led to the emergence of the Kashmir conflict.
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