Indians should brace for worse weather conditions as a major new storm brews in the Bay of Bengal off India's east coast on Thursday, forecasters cautioned, just days after one of the biggest cyclones to ravage the west of the country in decades left dozens of people dead.

The Indian Meteorological Department said, in its latest warning, that a cyclonic storm was on course to hit the eastern states of West Bengal and Odisha around May 26.

According to scientists, cyclones in the densely-populated region, which is also sagging under the burden of the COVID-19 pandemic, are becoming both more frequent and stronger as climate change causes warmer sea temperatures.

Cyclone Tauktae, which made landfall in the western Gujarat state on Monday night left a trail of destruction ripping out power pylons, damaging thousands of homes and blocking hundreds of roads.

The cyclone weakened into a depression as it moved across northern India, dumping heavy rain as it did so, including in Allahabad and New Delhi, which had its wettest May day on record.

Officials on Wednesday said the death toll in the state stood at 53 but the figure may be higher flowing reports by local dailies that close to 80 people had died in the state, with many killed by collapsing houses or walls.

Offshore oil installations were also hit with waves up to eight metres high, while one oil rig was dislodged, as were several support vessels with around 700 people on board.

Around 600 were rescued by the navy but 49 others died and 26 remain missing from an accommodation barge for oil workers that ripped free of its anchors in the storm and sank.

"We are lucky to be alive," one crew member told AFP after he left a navy destroyer in Mumbai on Wednesday.

"We were clinging onto the barge and luckily the life jackets helped us as the water was going over our head," he said.

Scientists have warned that cyclones in April and May before the monsoon season are becoming more common.

Last May, more than 100 people died after "super cyclone" Amphan ravaged eastern India and Bangladesh, wiping out villages, destroying farms and leaving millions without electricity.

However, as with other recent cyclones, the death toll was far lower than the many thousands killed in previous storms of that size, a result of improved weather forecasting and better response plans.

(With input from agencies)