Religious fanatics and radical minds issuing such threats should be immediately arrested, he posted on Facebook two days after Akhil Bhartiya Hindu Mahasabha leader Ashok Sharma reportedly said that people like Haasan should be "shot dead".
"Strongly condemn such criminal attempts against Kamal Haasan's freedom of speech by threatening to murder him by Hindu Mahasabha leader(s).
"Such religious fanatics and radical minds issuing murder/assassination threats should be immediately arrested by the concerned authorities an stringent legal action is needed against these persons who threatened to kill Kamal Haasan (sic)," Vijayan said.
"I strongly condemn anyone, following any religion or caste or gender, resorting to terrorism to accomplish their communal agenda to spread unrest in society and destabilise the country," he added.
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Meanwhile, Congress MP Shashi Tharoor tweeted, "I join @vijayanpinarayi in demanding arrest& prosecution of those inciting violence against KamalHaasan. #StopHate."
On November 2, Kamal Haasan had in his column in Tamil weekly 'Ananda Vikatan' claimed that right-wing groups have taken to violence because their earlier "strategy" has stopped working.
Sharma had reportedly said that those who make abusive remarks against Hindus should be punished. He had also called for a boycott of Hassan's films.