“They were transferred to a nearby medical facility but died from their injuries,” spokesman Lieutenant Colonel Davinder Anand said.
Kashmir is wholly owned by India and Pakistan, but only partly controlled by neighboring countries. Since the 1990s, Kashmir has been the site of a bloody rebellion against New Delhi.
India says Pakistan supports Kashmir militants. Islamabad denies this, saying it only provides diplomatic and moral support to the people of Kashmir.
Since the suspected militants killed three Hindus and a Sikh last week and triggered suppression by the Indian authorities, Muslim-majority areas have been on the fringe.
In northern Kashmir, security forces killed a suspected militant of the Resistance Front (TRF), which Indian police believe was behind a series of civilian assassinations supported by Pakistan.
Kashmir Valley Police Chief Vijay Kumar said the militant was suspected of killing a civilian driver and security forces had been looking for him after arresting four of his associates on Sunday.
“He was shot this morning,” Kumar said.
Kumar added that in another incident, another militant was killed in a gun battle in southern Kashmir.
Indian Army Chief of Staff Manoj Mukund Naravane said on Saturday that infiltration attempts by Pakistani militants have increased, and Pakistan agreed to a ceasefire with India along the Kashmir border in February.
“In the past month or so, we have seen new penetration attempts again,” Narawan told Channel India Today. “We have eliminated two or three such infiltration attempts.”