Vijayan was reacting to Rijiju's reported statement that Kerala had pressed for a ban on the PFI at the annual DGP conference held at Madhya Pradesh last month and Centre was considering it.
A statement from the Chief Minister's office, quoting Vijayan, said the state has not asked for a ban on PFI at the meet or on any other occasion.
It was not the government's policy to seek ban on communal organisations or extremist outfits, Vijayan said.
"It is not possible to face these organisations through banning them," he said, adding, past experience has proven it.
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"It is the same attitude in the case of PFI also," the chief minister said.
"The ideology of communal and extremist outfits and their threat will not cease to exist just by banning," he said.
Extremism has to be faced through stringent legal proceedings and mobilising people against it, Vijayan said.
He said the state government had initiated strong steps against communal and extremist forces, result of which was evident on the law and order front.
Only 14 cases were registered during 2013 and 2017, Vijayan said.
Facts prove that Kerala is at the forefront in safeguarding securalism, Vijayan said and pointed out that the National Crime Record Bureau documents collaborated this.
Meanwhile, the state police clarified that there was a presentation on the topic 'Radicalization-PFI' at the DGP meet but there was neither a suggestion nor any recommendation to impose ban on the PFI.
The presentation was prepared by a DGPs of a few states and presented by the Kerala DGP,a statement issued by the Police Information Centre said.