Officials said on Saturday that six fighters were killed after the army, acting on a tip-off, surrounded their hideout in the district of Pulwama, some 45km south of Srinagar.
Hiding in a residential area, the fighters reportedly opened fire as the army closed in.
“The fighting lasted for several hours and a few militants are believed to have escaped,” an army official said.
A spokesman for the Harkat-ul-Mujahidin group said its district commander and another district commander of the hardline Jaish-e-Muhammad were killed.
Three more fighters were killed in a separate encounter in southern Kashmir, army spokesman Colonel Bhanwar Rathore said.
Two Indian soldiers also died in the fighting.
Violence has swept Kashmir since 1989 when more than a dozen Kashmiri groups intensified their demand for the disputed region’s indepedence from Indian rule.
Official estimates suggest that up to 38,000 people have been killed in the conflict till date. The fighters put the toll much higher, at between 80,000 to 100,000.