Kumar said the killing of Kashmir's Hizbul chief Saifullah Mir was a major victory for India's counterinsurgency operations in the region.
Shortly after the gunfight, anti-India protests broke out in the neighborhood. Police fired tear gas and shotgun pellets to stop scores of stone-throwing young men from marching in the area.
Kashmir is divided between India and Pakistan, but the rivals each claim the region in its entirety. Rebels have been fighting against Indian rule since 1989. Most Muslim Kashmiris support the rebel goal that the territory be united either under Pakistani rule or as an independent country.
India says Kashmir militancy is Pakistan-sponsored terrorism. Pakistan denies the charge, and most Kashmiris call it a legitimate freedom struggle.
There was no immediate confirmation from the rebels about the killing.