Militants on Sunday threatened to kill Sopore municipal chairman Ghulam Rasool Dar's son, whom they have kidnapped, if he did not step down by Monday.
Police said militants kidnapped Mehraj-ud-Din, 12, while he was playing cricket in Mehrajpora locality of Sopore town in north Kashmir's Baramulla.
Dar had won the recent civic poll as a Congress candidate.
He told the police that the abductors of his son had phoned his residence.
Militants have so far gunned down nearly half a dozen councillors across Kashmir, prompting the government to provide security to other councillors.
The councillors have said that the one armed guard provided to them is inadequate for their security.
