The naval ships, which left from the Southern Naval Command here yesterday, are likely to reach Lakshadweep this evening.
The spokesman said about eight boats from Kerala with 36 people on board are reported to be adrift at sea off Kalpeni island.
"The sea is very rough.. Naval ships moved as soon as we received intimation," he said.
Fifteen fishermen rescued by the Coast Guard are being brought to the Thiruvananthapuram coast, the official said.
Four fishermen were rescued by a Navy chopper this morning, 20 miles off Kochi.
Fishermen rescued from a capsized boat by the combined effort IAF, Indian Navy and Indian Coast Guard. Photo source: Twitter
They were taken to a naval clinic here for medical examination.
INS Nireekshak rescued two fishermen off Alappuzha coast.
INS Sagardhwani fished out one cadaver, 30 km off Thiruvananthapuram coast.
The ship had earlier found another cadaver.
The body has been handed over to the civil administration, he said.
Indian Coast Guard ship Samar rescued a fishing boat with five crew members on board, the spokesman said.
He said one of the crew in an advanced light helicopter (ALH) was wounded while assisting fishermen trapped in the sea off Kerala coast.
The crew member, V K Verma, suffered hand injury caused by the winch wire.
Indian Coast Guard continues Cyclone Ockhi response with 09 Ships and 02 Dornier Aircraft off Kerala and Tamil Nadu Coast. Photo source: Twitter
He, however, continued "heroically" to help the fishermen to be rescued, before himself being winched up, the spokesman said.
Verma has been admitted to a hospital in Thiruvananthapuram.
The 'very severe' cyclonic storm Ockhi -- which in Bengali means 'eye' -- is likely to continue to move west-northwestwards across Lakshadweep islands during the next 24 hours and then recurve northeastwards during the subsequent 48 hours, a Met department bulletin said.