Kashmir police inspector general Vidhi Kumar Birdi told AFP that authorities in the disputed territory had "carried out two different operations" in villages in the Kulgam district, The Bussiness Standard reported.
Birdi said two members of the security forces had been killed, with clashes continuing in Modergram and Frisal Chinnigam villages.
"We have retrieved the bodies of two terrorists from Modergram, and four others from Frisal Chinnigam," said Birdi.
This is the latest incident in an uptick of attacks in the disputed territory.
India and Pakistan both claim Muslim-majority Kashmir in full and have fought three wars for control of the Himalayan region.
Rebel groups have waged an insurgency since 1989, demanding independence for the territory or its merger with Pakistan.
The conflict has killed tens of thousands of civilians, soldiers and rebels.
In June, nine Indian Hindu pilgrims were killed and dozens wounded when a gunman opened fire on a bus carrying them from a shrine in the southern Reasi area.
It was one of the deadliest attacks in years and the first on Hindu pilgrims in Kashmir since 2017, when gunmen killed seven people in another ambush on a bus.
SD/PR