Soldiers and special operations officers cordoned off Panzgam village, about 35 kilometers (22 miles) south of the main city of Srinagar, before dawn after receiving a tip off that militants were hiding inside a house.
"The operation started in the night in which three terrorists were killed," Colonel N. N. Joshi, an army spokesman, told AFP.
As word of the killings spread, hundreds of villagers came out onto the streets, throwing stones at police who fired tear gas to disperse the crowd, an officer said on condition of anonymity.
Police later identified the deceased as members of Hizbul Mujahideen, a local rebel group opposed to Indian rule of Kashmir.
Kashmir has been divided between India and Pakistan since the end of British colonial rule in 1947. Both claim the Himalayan territory in its entirety.
Hizbul Mujahideen is one of several rebel groups that have since 1989 been fighting Indian forces deployed in the disputed region, calling for independence or a merger of the region with Pakistan.
The fighting has left tens of thousands dead, mostly civilians.
Since the beginning of the year, residents have frequently taken to the streets to support rebels following gun battles with government forces.
Two civilians have died in the resultant clashes and scores have been injured since February.
Civil and military authorities have issued repeated warnings asking people within a two kilometer-radius of a gun battle to stay indoors, but the warnings have mostly been ignored.
On Friday an Indian soldier was killed trying to stop suspected rebels from crossing the de facto border with Pakistan.
India regularly accuses Pakistan of arming rebels and sending them across the border.
Islamabad denies the allegation, saying it only provides moral and diplomatic support to the Kashmiri struggle for right to self-determination.