The United News of Bangladesh said rescuers had recovered at least 19 bodies on Wednesday along the Bay of Bengal after sudden squalls hit the country's southern coast.
About 900 other people, including a naval commander, were missing after the storms started late on Tuesday, the news agency reported, quoting coastguards, boat owners and survivors.
Coastguards and rescuers found the bodies of 15 fishermen washed ashore in Bagerhat district, 137km south of the capital, Dhaka. Three bodies were found in neighbouring Patuakhali, and one in Barguna.
Passing ships and trawlers also rescued dozens of fishermen afloat in the sea or stranded on coastal islands, the agency said.
A navy ship partially overturned at Akram Point in Khulna during the storm, leaving its commanding officer missing, but about 40 others aboard the ship are safe, the report said.
The coastguard has deployed helicopters to search for Lieutenant Commander Firoz Kabir, the report said, citing coastguard official Badruddoza Chowdhury.
The chief of the Cox's Bazar fishing boat owners' association meanwhile said he feared at least 30 fishing boats carrying dozens of fishermen capsized in the major coastal district.
"We are trying to assess the exact number of fishermen missing in Cox's Bazar," Mujibur Rahman said.