A Belize-registered timber-carrying cargo vessel was reported sinking in the Bay of Bengal near the east Indian port city of Haldia, officials said on Tuesday.
Indian Coast Guard officials said the ship began sinking after cracks developed in its hulk.
West Bengal state coast guard commander RK Wadha said the ship developed cracks at the sandheads of Haldia port, about 175 kilometres south of Calcutta.
The 20 crew members -- 17 from the Philippines, two from Myanmar and one Indonesian -- were rescued by a ship of the Indian Shipping Corporation and hovercrafts of the coast guard, he said.
The engine room of the ship had been flooded as water continued to gush into the ship through the cracks, he said.
The ship, M V Fortune, carrying 5,203 tonnes of logs, was heading to Calcutta harbour from Penang in Malayasia.
The hulk of the ship developed cracks after a number of logs fell off and dashed against the ship following a storm on Monday night, Wadha said.
"We received wireless messages from the sinking ship in the morning. Coast guard hovercrafts flew to the spot and asked the crew members to abandon the ship at about 11 am (0530 GMT)," he said.
The Indian Shipping Corporation's Mt Lokmanya Tilak also rushed to the scene, he said.
"All inbound and outbound ships have been warned as the logs have drifted away," he added.
Last month, an Indonesian ship sank off the eastern coast near Calcutta, spilling tonnes of oil and soda ash into the sea.