It has piled pressure on Indian authorities as they grapple with a massive rise in coronavirus infections and deaths as well as a shortage of beds and oxygen in hospitals.
"This is one of the most challenging search and rescue operations I have seen in the last four decades," Murlidhar Sadashiv Pawar, Deputy Chief of Naval Staff, told Reuters partner ANI on Tuesday.
Navy spokesman Vivek Madhwal said waves reached 20 to 25 feet amid poor visibility. Three more barges were adrift near the Gujarat coast but rescue operations were underway.
The storm made landfall in Gujarat state late on Monday and was expected to weaken overnight into Wednesday, the Indian Meteorological Department said.
"... weather conditions are expected to return to normal by tomorrow (Wednesday)," Gujarat Chief Minister Vijay Rupani said.
He said 160 state roads had been destroyed, 40,000 trees uprooted and several houses damaged by the cyclone.
Navy spokesman Madhwal said five ships backed by surveillance aircraft were scouring the site of the sinking of the barge "P305" in the Bombay High oilfield, where the country's biggest offshore oil rigs are located.
On Monday, the crew sent an SOS that the ship had lost control as the cyclone roared past Mumbai. Naval ships were sent to the area and on Tuesday, as the barge started sinking, many of the crew were rescued from the sea.
The oilfields are around 70 km (45 miles) southwest of Mumbai. The barges are deployed by Afcons Infrastructure Limited, a construction and engineering company based in Mumbai, and were engaged in contract work awarded by Oil and Natural Gas Corp (ONGC), India's top exploration company.
"P305 had a full complement of safety equipment including life jackets and life rafts for all persons on board. We believe all personnel safely evacuated before the vessel sank," Afcons said in a statement late on Tuesday.
The storm caused damage to several of the vessels deployed, the company said, adding that every effort was being made to rescue the missing personnel.
ONGC said in a statement it was extending help to the navy and coastguard in the rescue effort.
More than 200,000 people were evacuated from their homes in Gujarat before the arrival of Tauktae, which packed gusts of up to 210 kph (130 mph).
No damage was reported at refineries in Gujarat or at sea ports located in the storm's path. Operations at India's largest private port, Mundra, have resumed, a port official said.
(Additional reporting by Aishwarya Nair and Sudarshan Varadhan; Writing by Sanjeev Miglani and Nupur Anand; Editing by Himani Sarkar, Alex Richardson, Nick Macfie and Gareth Jones) ((firstname.lastname@example.org; +91 11 49548038; Reuters Messaging: email@example.com@reuters.net))