People attempt to remove uprooted trees from the entrance of a residential building in Mumbai. Reuters

A monster cyclone was lashing India on Tuesday, with powerful winds and driving rain leaving at least 21 people dead, and interrupting the vaccine programme the country urgently needs to get its spiralling Covid-19 outbreak under control.

Cyclone Tauktae battered swathes of the vast nation, sending huge waves crashing onto its shores, turning streets into rivers and forcing hundreds of thousands of people to flee.

At least 96 were missing on Tuesday, compounding the misery for millions of others who are enduring a devastating coronavirus surge.

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The Indian navy is working to rescue crew members from a sunken barge and a second cargo vessel that was adrift Tuesday off the coast of Mumbai after a deadly cyclone struck the western coast.

A man walks past a fallen tree on a street following heavy rains from Cyclone Tauktae in Mumbai. AFP

The navy said it had rescued 177 people of the total 400 on the two barges in the Arabia Sea. Three frontline warships were part of the rescue operations and were scouring seas, the Navy said.

Both barges are owned by Oil and Natural Gas Corporation, the largest crude oil and natural gas company in India.

The colossal swirling system -- the biggest to hit the region in decades -- claimed lives in Kerala, Goa, Maharashtra and Gujarat as savage winds swept through flimsy homes and uprooted trees and electricity pylons.

A man removes debris from his damaged shop in Amreli on Tuesday, after Cyclone Tautae hit India. AFP

Mumbai authorities closed the airport and urged people to stay indoors, shifting about 600 Covid-19 patients in field hospitals "to safer locations", while sea levels swelled as high as three metres (10 feet) near the seaside town of Diu.

Two navy ships were deployed to assist in search and rescue operations for a barge carrying 273 people adrift off Mumbai's coast, with 28 picked up so far, the defence ministry said late Monday.

Tauktae made landfall in Gujarat on Monday as an Extremely Severe Cyclonic Storm packing gusts of up to 185 kilometres (115 miles) per hour, the Indian Meteorological Department said. It had been downgraded to a Very Severe Cyclonic Storm by Tuesday morning.

People move a fishing boat to a safer place along the shore ahead of Cyclone Tauktae in Veraval, Gujarat. Reuters

Hundreds of thousands of people were without power after Cyclone Tauktae, one of a growing number of increasingly severe storms in the Arabian Sea blamed on climate change, hammered the Gujarat coast on Monday evening.

The cyclone packed gusts of up to 185 kilometres (115 miles) per hour, uprooting trees and knocking down power lines and mobile phone towers as it barrelled inland while weakening slightly.

One support vessel serving oil rigs that were hit by immense waves off the coast of Mumbai sank and 96 of the 273 people who had been on board were missing, the Indian Navy said Tuesday.

The defence ministry said 177 people were rescued from the vessel, with operations expected to continue throughout the day in "extremely challenging sea conditions".

The National Disaster Response Force personnel clear fallen trees from a road in Goa. AFP

Elsewhere one fresh casualty was reported on Tuesday, taking the confirmed death toll to at least 21 as savage winds swept through flimsy homes and turned streets into rivers.

Although the cyclone was one of the fiercest to hit the area in decades, better forecasting than in recent years allowed for strong preparations, and more than 200,000 people in danger zones were evacuated from their homes.

Mumbai authorities on Monday closed the airport for several hours and urged people to stay indoors as huge waves battered the city's seafront.