At least 146 personnel were rescued so far from the barge P305 which is sunk on-site, ANI reported.
The aerial search commenced at first light with Indian Navy P8I on task, the Defence PRO informed.
Barge P305, an accommodation barge of the state-run Oil and Natural Gas Corporation (ONGC), capsized off Heera oil fields in Bombay High on Monday night after the impact of Cyclone Tauktae broke its mooring and set it adrift. It was steadied later.
ONGC carries on offshore drilling from platforms in the Arabian Sea. As per a recent media report, the company produces 50,000 barrels of crude per day from the Heera platform. Typically, staff are taken for offshore drilling operations by air.
Six persons were killed in Maharashtra's Konkan region in separate incidents related to the severe cyclonic storm and three sailors remained missing after two boats sank in the sea, officials said.
Three persons died in Raigad district, a sailor in Sindhudurg district and two persons were killed in Navi Mumbai and Ulhasnagar in Thane district after trees fell on them.
Two boats with seven sailors on board, anchored in the Anandwadi harbour in Sindhudurg district capsized, an official statement said.
As the cyclone moved past the Maharashtra coast in the morning, Mumbai's Chhatrapati Shivaji Maharaj International Airport initially announced the suspension of operations from 11 am to 2 pm and later decided to keep all operations shut till 8 pm.
Over 1.5 lakh people were shifted from low-lying coastal areas in Gujarat, while 54 teams of the NDRF and SDRF remained deployed, an official said.
Gale-force winds, heavy rainfall and high tidal waves swept the coastal belts of Maharashtra and Goa as Tauktae hurtled northwards towards Gujarat.
Winds blew at 114 kmph in Mumbai on Monday afternoon as the cyclonic storm passed close to the Mumbai coast, civic officials said.
The highest wind speed of 108 km per hour was recorded at the Colaba observatory in the afternoon, said Shubhangi Bhute, senior director, IMD Mumbai.
Maharashtra Chief Minister Uddhav Thackeray on Monday took stock of the situation in Mumbai, Thane and other coastal districts of the state in the wake of the cyclonic storm.
As Mumbai and other coastal areas continued to be battered with heavy rains, over 12,000 people were relocated to safer places from the coastal areas. These include 8,380 people in Raigad, 3,896 in Ratnagiri and 144 in Sindhudurg districts.
(With inpputs from agencies)