Muhammad Maqbul Shah, who belonged to the main opposition National Conference, was shot outside a mosque in the state's summer capital Srinagar on Wednesday, according to police.
Shah won a councillor's seat during the 1 February civic elections and was a frontrunner for the mayor's job in Srinagar.
In southern Rajouri district, Indian troops shot dead four suspected separatists inside a cave in southern Rajouri district, police said.
Police in Srinagar also resorted to firing teargas shells to disperse people gathered to protest the gunning down of a car mechanic on Sunday by paramilitary Border Security Force soldiers, witnesses said.
Hundreds of protestors shouting pro-Islamic and anti-government slogans poured onto the streets of Srinagar's Miasuma locality and forced shops to pull down their shutters.
Kashmir is witnessing an insurgency against Indian rule that has so far left more than 40,000 people dead by the official count. Separatists put the toll twice as high.