Maritime ports of Chattogram, Cox's Bazar, Mongla and Payra have been advised to keep hoisting distant warning signal number two.
Cyclonic storm "Bulbul" over the east-central bay and adjoining area moved north-northwestwards on Thursday morning.
It was centred at about 930km south-southwest of Chattogram port, 855km south-southwest of Cox's Bazar port, 910km south of Mongla port and 865km south of Payra port, the Met Office said in a special weather bulletin.
It is likely to intensify further and move in a north-northwesterly direction.
The maximum sustained wind speed within 54km of the cyclone centre is about 62kph rising to 88 kph in gusts or squalls. The sea will remain very rough near the cyclone centre, the Met Office said.
All fishing boats and trawlers over North Bay and deep sea have been advised to remain close to the coast and proceed with caution until further notice.
They have also been advised not to venture into the deep sea.