Police said on Sunday that fighters attacked a house in Udhampur district, south of capital Srinagar, and shot dead a woman, her daughter and an infant.
In other incidents, suspected separatist fighters shot and killed an activist of India's ruling Congress party in Anantnag district, Also, two civilians were shot dead and two beheaded by fighters in the past 24 hours.
Elsewhere, Indian troops killed two senior commanders of a dominant separatist group overnight.
A police spokesman said on Sunday that Ghulam Mohammed Malik and Mohammed Ashraf Padder were shot dead in separate clashes in northern Kupwara and southern Anantnag districts.
"Both were senior commanders of Hizbul Mujahidin and were on the security force list of most wanted militants," he added.
Hizbul Mujahidin was one of the first separatist groups to launch an insurgency against Indian rule in Kashmir in 1989.
The violence comes as India and Pakistan, who have fought two wars over the disputed Himalayan region, are preparing to start a bus service linking the two parts of divided Kashmir on 7 April.