The killings came three days before polling for south Kashmir's Anantnag constituency which the district is part of.
A senior police officer said guerrillas opened fire at Ghulam Nabi Mir, sarpanch of Batgund village near Tral town, 45 km from here, near his home, critically injuring him and his son identified as Firdaus Ahmad.
"Mir and Firdaus were taken to hospital where both succumbed to their injuries," the officer said.
Earlier, militants also fired at Anwar Sheikh, headman of Amler village, near his home. "Sheikh succumbed to injuries while being taken to hospital," the officer said.
Last week guerrillas had killed a sarpanch in a village adjoining the highway town of Awantipore in the same district, leading to panic among the local elected village heads, some of whom have announced their resignations from their posts.