Ashiq Hussain, a police officer, said security forces fought suspected Muslim fighters, killing two of them in Laddu, a village 95km south of Srinagar, the summer capital of India's Jammu-Kashmir state.
Hussain said the slain fighters belonged to the largest Kashmiri separatist group, Hizb-ul-Mujahidin. There was no independent confirmation of his claim.
Meanwhile in a nearby village, unidentified armed men abducted a policeman from his home early on Monday and later killed him in a rice field, Hussain said. Police blamed Muslim fighters.
Also on Monday, police said they killed another suspected Hizb-ul-Mujahidin fighter in a gunfight in Chandyari, a village nearly 300km southwest of Srinagar.
On Sunday, three suspected separatists were arrested during a raid in Pulwama, 50km south of Srinagar.
Several pistols, grenades and 2kg of explosives were recovered from the separatistl hideout, the statement said.
More than a dozen Muslim separatistl groups have been fighting government forces for Kashmir's independence from India or against its merger with Pakistan since 1989. The insurgency has claimed more than 66,000 lives.