The boat 'Dutta Sai', carrying 17 fishermen, had sunk about 30 nautical miles west of Mumbai in the sea at around 4 am on Saturday due to bad weather.
While 14 fishermen were rescued on Saturday, two Naval divers were deployed to locate the others.
However, the divers also went missing on Saturday night amid the rough waters. They were rescued on Sudnay morning, a release from the Indian Coast Guard said, adding the three fishermen are still missing.
'MV Dependable', a merchant ship had rescued the 14 fishermen. The search and rescue operation was conducted by the units of Coast Guard, Navy and ONGC, it said.
During the search operation, 'INS Trishul' spotted a fisherman in the evening, following which the ship lowered a boat and two divers went to pick up the survivor.
However, both the survivor and the divers could not be seen even at close range by the ship due to rain, bad weather and darkness, the release said.
Search efforts have been stepped up to locate the three missing fishermen, it added.