The Kerela chief minister said he told the Prime Minister that he was ready to take any step to ensure that peace prevailed in his state.
Addressing a press conference at Kerala House, Vijayan said the Prime Minister raised the matter during the meeting and expected him to intervene and end political violence in the state.
To this, Vijayan replied that both the parties should restrain their workers from engaging in conflicts.
Vijayan said that he would discuss the issue with his Cabinet colleagues and party leaders.
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He expressed the hope that the central government will help the newly-elected Left Democratic Front for development of the state.
On Mullaperiyar dam issue, which has been a bone of contention between Kerala and neighbouring Tamil Nadu, Vijayan said a solution to the problem could be found only through a democratic process.
"Conflict cannot solve the issue so democratic process need to be followed for a solution," he said, adding, his government will go through reports of various commissions before its next step.