A defence spokesman said on Firday that the three were killed when the army on a tipoff launched an operation to "dismantle" a hideout of the fighters in Udhampur district, some 120km north of Jammu.
"The militants fired on us when we encircled the hideout. Three militants have been killed so far. We think that four more militants are still holding out," the spokesman, Lieutenant Colonel B.S.Rathore said.
Mufti Mohammed Sayeed, the chief minister of the provincial government, has meanwhile ordered a judicial probe into the alleged custodial death of a Kashmiri, who was reportedly detained by the security forces a day after his wedding last week.
Indian army officials say Tahir Hussain was killed in an explosion as he led soldiers to a Kashmiri separatist group's hideout.
But his death sparked widespread protests, prompting the chief minister to visit his village to pacify villagers.
Promising a truthful inquiry into the circumstances leading to Hussain's death, Sayeed said the guilty would be punished.
"I have made things abundantly clear to the army, paramilitary and the police that they should ensure protection of the innocents while dealing firmly with militants," the chief minister said.