Indian police also used force and fired pellets on people during a protest against the killings in the area.
Paramilitary officer Nalin Prabhat said the fighting erupted in the southern Pulwama area following reports that some militants were hiding there.
He said the rebels hurled grenades and sprayed gunfire at the soldiers in an attempt to escape before they were shot dead. Government forces were searching for a third insurgent who they believed fled during the fighting.
Police identified the slain one youth as Manzoor Ahmad Dar of Gandibagh Kakapora.
Hundreds of residents of nearby villages clashed with troops in support of the rebels. Police fired tear gas to disperse the rock-throwing protesters. No injuries were reported.
Rebel groups have been fighting for Kashmir’s independence from India or its merger with neighboring Pakistan. Kashmir is divided between India and Pakistan, which both claim the entire region.
Meanwhile, Indian troops barged into the houses and beat up inmates without any reason at Kulpora in Kulgam district. The victims said that the Indian army personnel also smashed windowpanes of two mosques in the village.