Security forces killed two Muslim fighters in Baramulla district near the northern ceasefire border, known as the Line of Control, the spokesman said, adding that five other rebels were killed in Pulwama district just south of the summer capital Srinagar on Sunday.
"Two of the slain militants were from the hardline Jaish-e-Muhammad rebel group," he said.
In another incident, according to the police spokesman, suspected separatists on Saturday shot dead Zahur Ahmad, an official from the state's ruling People's Democratic Party, in Tailbal, on the outskirts of Srinagar.
None of the dozen-odd separatist groups fighting Indian rule in Kashmir claimed responsibility for the killing.
Surge in violence
Rebels often target pro-India politicians and people they suspect of working for Indian troops.
At least 37 people have died over
the past week in the Indian zone
Over the past week at least 37 people have died in Indian Kashmir - 19 rebels, 14 civilians and four security force personnel according to police figures.
About 44 people were injured, 16 of them security force personnel.
The spurt in violence comes before Thursday's planned resumption of a bus service linking the Indian and Pakistani zones of Kashmir, a step regarded as a key confidence-building measure between the two nuclear-armed rivals.
Rebels are opposed to the bus service, which came to a halt when India and Pakistan fought their first war over Kashmir in 1947, saying it only serves to "strengthen the Indian occupation" of the Himalayan region.
The neighbours hold Kashmir in part but claim it in full, and have fought two of their three wars over the region, where a separatist insurgency has raged since 1989, leaving tens of thousands dead.
Four rebel groups have warned Kashmiris not to ride the bus, describing the vehicle as a "coffin".