Vijayan, the chief minister, has requested extra funding as well as 20 more helicopters and 600 motorised boats to step up the rescue efforts.
"The death toll has risen to 373", an official of the state's disaster management authority told Reuters.
More than 400 people have died since the monsoon started in May. The season runs from June to September. With the weather department expecting rains to continue into the weekend, the state remains on high alert.
At least 1,000 were feared stranded in five villages around Chengannur, one of the districts worst hit by the deluge.
Indian health authorities said they were focusing on preventing the spread of disease.
Keeping up with the flood relief efforts, Indian Navy station INS Garuda on Monday witnessed the operation of civilian flights in order to compensate for the flooded Nedumbassery airport (Kochi).
"The biggest challenges immediately ahead are cleaning the flood-hit houses, rehabilitation, and prevention of water-borne diseases", said Mahesh P., a village-level officer from Rayamangalam, some 45 kilometers (28 miles) from Kerala's financial capital of Kochi.
Kochi's main airport has been closed since last week due to the severe flooding.
Prabhu said on Twitter that other air bases around Kerala should open to commercial traffic soon.
The floods have caused an estimated $3 billion in damage but the bill is likely to rise as the scale of devastation becomes clearer.
Kerala state is home to 33 million people and is known for its tourist beaches and hill resorts.