The Bangladeshi navy says it is searching for dozens of fishermen still missing after a powerful storm.
Cyclone Mora, which brought high winds and torrential rain, killed seven people and destroyed thousands of homes when it hit on Tuesday.
The areas around Cox's Bazar and Chittagong, along the border with Myanmar, bore the brunt of the storm.
Camps on the border housing thousands of Muslim Rohingya refugees from Myanmar were badly damaged.
Fishing vessels were ordered back to port as the storm approached, but a local fishing industry representative said about 150 people were missing.
The Bangladeshi navy said it had sent 15 ships to search for survivors and had so far rescued at least 20 fishermen.
The Indian navy picked up 33 survivors on Wednesday but Indian officials said it was not clear whether they came from vessels that had sunk or from huts washed into the sea.
The Bangladeshi fishing industry representative, Mushtaq Ahmed, told Agence France-Presse news agency that if these survivors were rescued fishermen, then some 90 would still be missing.
"They could be moored on an island or adrift at sea," he said. "In the past we have seen that most of the fishermen return to their fishing ports within a week or two. We hope this time they will also be back in good health."
He said many of the boats that did return to port had been damaged by the storm.
Around 350,000 people were evacuated from low-lying areas ahead of Cyclone Mora's arrival. A local official said 50,000 homes had been destroyed or damaged by the storm in Cox's Bazar.
The area is home to camps for hundreds of thousands of Muslim Rohingya refugees who have fled violence in neighbouring Myanmar.
"Housing for undocumented Myanmar nationals near Cox's Bazar was severely damaged," the Office of the UN Resident Co-ordinator for Bangladesh said. "Rohingya refugees are currently without reliable shelter, food and fuel."
Sanjukta Sahany, local head of the International Organisation for Migration, told AFP that more than 16,000 homes in the camps had been destroyed or damaged.
The cyclone blew in from Sri Lanka, where it caused flooding and landslides that killed 202 people. Another 96 people are listed as missing.