The separatists were killed in Tangdhar north of the main city of Srinagar after crossing over from the Pakistani side of the heavily militarised border that divides the area between the two countries, it said.
“Three terrorists were killed in the fight. Three assault rifles were also recovered from the site of the gun battle,” army spokesman Colonel N.N. Joshi told AFP.
The army was trying to determine if the separatists were part of the same group that attacked an Indian ammunition depot in the area on Friday, injuring at least three border guards.
Indian Kashmir has been under curfew since protests erupted over the death last month of a popular young separatist leader, Burhan Wani, in a gunfight with security forces.
More than 60 civilians have been killed in clashes between protesters and security forces, and thousands more injured in the worst violence to hit the Himalayan region since 2010.
Wani’s Hizbul Mujahideen and several other separatist groups have fought for decades an estimated 500,000 Indian soldiers deployed in the territory, demanding independence for the region or its merger with Pakistan.