The death toll from Cyclone Bulbul rose to 12 in Bangladesh and five fishermen are still missing, government officials said on Monday.
Most of the victims had refused to evacuate and died due to falling trees, said Enamur Rahman, Bangladesh's junior minister for disaster management and relief.
One fisherman drowned and five were missing after their boats capsized on Sunday due to strong winds and currents, authorities said. Another 30 fishermen were rescued.
Around 6,000 homes were partially or fully damaged. No major damage was reported in camps in southeastern Bangladesh where hundreds of thousands of refugees from neighbouring Myanmar are living.
A ship will sail to St. Martin's Island on Monday to rescue 1,200 mostly local tourists who have been stranded there for days, said Saiful Islam, the chief executive of Teknaf sub-district.
In India's state of West Bengal, seven people were killed, Javed Khan, the state's minister for disaster management told reporters on Sunday evening.
The cyclone season in the Bay of Bengal can last from April to December. In 1999, a super-cyclone battered the coast of India's Odisha state for 30 hours, killing 10,000 people.