Such forces are a "danger" to the state, Vijayan said, replying to an adjournment motion moved by Indian Union Muslim League (IUML) legislator, Parakkal Abdulla, seeking a debate on the recent murder of a league activist at Kuttiyadi in Kozhikode district.
The government had an open mind on the issue. The murder was "pre-planned" and a thorough investigation was needed, he said, adding, the matter should be treated seriously.
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"We will also look if SIT (Special Investigation Team) is needed to be constituted. If there are any lapses on the part of police on investigation of the case, strict action will be taken," Vijayan said.
On the allegation that police had hosted lunch for some of the accused in the case at a police station, Vijayan said the allegation needed to be probed.
"If such an incident did happen, action will be taken. Government will not compromise on the issue, which is a serious matter," he said.
Opposition leader Ramesh Chennithala said the attack on the IUML worker was "well-planned."
Alleging that RSS and SDPI are giving leadership to such violence, he said "they are two sides of the same coin."
He also alleged that the chief minister was taking a 'soft stand' towards SDPI in the Kuttiyadi incident.
"IUML is taking a stand against extremism and all political parties should unitedly fight against such forces in the state," he said.
Alleging that police had been 'inactive' since LDF came to power, he said there has been 40 murders, 48 murder attempts and over 400 attacks on women, he said.
Abdulla alleged that the IUML worker Nasaruddeen was killed in broad daylight by SDPI activists."Government is shying away from taking action against SDPI, which is allegedly supporting IS activities in the state."
After Speaker P Sreeramakrishanan declined permission for a debate on the issue, Opposition Congress-led UDF walked out.