Millions have been evacuated as heavy rains and winds lash the country's southeastern coast, prompting authorities to raise the weather warning to its highest level.
Up to a million people are facing evacuation in Bangladesh after a powerful cyclone made landfall in the southeastern coastal region.
Cyclone Mora is packing winds of up to 100 kilometres an hour (60 mph) and has prompted authorities to raise the weather warning to its highest level.
Cyclone Mora struck the island of Saint Martin and Teknaf in the coastal Bangladeshi district of Cox's Bazar, where officials said some 200,000 people were evacuated to shelters. In Chittagong district, about 150,000 people were evacuated.
The cyclone also battered refugee camps in Bangladesh where hundreds of thousands of Rohingya Muslims from Myanmar have taken shelter from persecution at home.
Shamsul Alam, a Rohingya community leader, said damage in different camps was severe. Almost all the 10,000 thatched huts in the Balukhali and Kutupalong camps were destroyed, Alam said.
Officials in Chittagong reported winds gusting up to 135 kph (85 mph), and said low-lying coastal areas were flooded by a storm surge with waves 2 metres (7 ft) high.
Flights in the area were cancelled.
A UN official working with Rohingya refugees in Bangladesh said the damage in the camps could not be assessed while the storm was raging.
"The winds are strong and people there live in flimsy structures, so we're worried."
However, Bangladeshi weather officials said the cyclone was not as bad as they had feared.
Threat of waterborne diseases increases in Sri Lanka
Thousands of survivors of devastating floods and landslides in Sri Lanka are at risk of potentially fatal diseases such as dengue fever, charities warned on Monday as the death toll from the cyclone's passage across the island continues to rise.
Flooding and mudslides have claimed the lives of at least 180 people and left nearly half a million people displaced in southwestern Sri Lanka.
More than 100 people are still missing.
Rescue operations are under way, and international aid has started to arrive after the government asked for help.
India braces for Cyclone Mora
The cyclone was expected to weaken in Bangladesh by late Tuesday morning as it moved inland towards India, where authorities have warned of heavy rain in the northeastern states of Tripura, Mizoram, Manipur, Nagaland and Arunachal Pradesh.
The cyclone formed after monsoon rains triggered floods and landslides in Sri Lanka, off India's southern tip.
In the eastern Indian state of Bihar, 24 people have been killed in recent days, either by lightning or in collapsed dwellings.
The monsoon reached the Kerala coast of southwestern India on Tuesday.