The death toll in the disaster has, meanwhile, climbed to 58 with more bodies recovered from high seas.
State control room officials said three bodies were found off the coast of Kozhikode and three from Kochi.
Union Defence Minister Nirmala Sitharaman has agreed to continue the search operations in the high seas as requested by the state, Vijayan told reporters here after a Cabinet meeting.
However, the chief minister said complete information was still not available on the fishermen who went out to sea during the cyclone days.
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When pointed out that the Latin Catholic Church, to which most of the affected fishermen belonged, had disputed the official figure on missing fishermen, Vijayan said, "there is no need for dispute on that."
The government has a figure of missing persons and if there were any more persons other than in the list, that also would be confirmed, he added.
The official missing toll is 94.
In a bid to set up a mechanism to ensure safety of fishermen, Vijayan said a system was being planned in association with the Indian Space Research Organisation (ISRO).
The financial assistance of Rs 20 lakh for families of fishermen killed in the cyclone would be given in one go, he said adding "it will be given shortly without any hassle."
An amount of Rs five lakh would be given to those who were seriously injured and not able to go for work in future as an "alternative livelihood" initiative, he said.
Efforts were on to identify the bodies through DNA test, he said.
Observing that the Centre seems to have understood the gravity of the damage caused by the cyclone in the state, Vijayan said Union Home Minister Rajnath Singh has assured him that a Central team would visit the affected areas very soon.
He appealed to government employees to donate three days salary and workers in other sectors one day's salary to the fund.
Giving details of the measures planned for the victims, he said houses would be built for those who had lost it under the government's Livelihood Inclusion and Financial Empowerment (LIFE) programme.
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