Hundreds of thousands of people in Bangladesh have been evacuated, as Cyclone Mahasen hit one of the poorest countries in Asia with winds of around 100km per hour.
Similar measures have been taken in Myanmar however, some displaced people, most of them Rohingya Muslims, in Rakhine state have ignored calls for them to evacuate camps.
The UN said that more than 4.1 million people could be at risk from the cyclone, which crossed Bangladesh's low-lying coast on Thursday.
Mahasen first hit Khepupara on the southern coast and then weakened as it headed northeast towards the ports of Chittagong and Cox's Bazar.
Witnesses told the Reuters news agency that low-lying coastal areas were covered in waist-deep water, trees were uprooted and houses damaged.
Media reports said five people were killed, some by falling trees, and thousands of rickety huts were destroyed as the storm brought torrential rain.
Meteorologists said Mahasen should weaken quickly into a tropical rain depression over land.
"Mudslides will also be a concern as the heavy rain spreads farther north and east on Thursday night and Friday into easternmost India and northern Myanmar," said meteorologists at Accuweather.com storm forecasters.
Bangladesh evacuated more than 700,000 people living in the low-lying areas to thousands of cyclone shelters on Wednesday, while Myanmar announced plans to relocate about 166,000 people on its northwest coast.
Our special correspondent, whom we are not naming because of reporting restrictions, said the Bangladesh government was alerting its citizens via community radio and text messages and had set up roughly 3,000 shelters.
Bangladesh, where storms such as the Cyclone Nargis in 2008 have killed many people, has more than a thousand cyclone-proof buildings.
The country is maintaining its storm warning to seven, on a scale with a maximum of 10.
On Tuesday, the storm killed at least seven people and displaced thousands in Sri Lanka as it tracked across the Bay of Bengal towards Bangladesh.
Operations at the local airports in Chittagong and Cox's Bazar were suspended. Shops were shuttered and roads were empty except for a few cars and rickshaws before the storm hit.
|Tropical Cyclone Mahasen weather explainer
In Myanmar's state of Rakhine, many Rohingya Muslims made homeless by communal bloodshed last year said they were too scared to move, reflecting their deep mistrust of the authorities and of local Buddhists.
But after Wednesday's heavy rains, many Rohingya at camps loading their belongings into trucks provided by the humanitarian groups.
Al Jazeera’s Wayne Hays, reporting from Sittwe, said that Myanmar might have escaped the worst as Mahasen appears to have missed it. But he said evacuations are continuing and many are seeking refuge in schools, clinics and mosques.
Buddhist-Muslim clashes in the region last year left about 200 people dead and whole neighbourhoods burned to the ground.
The danger faced by those trying to flee was underlined on Monday when 58 Rohingya were left missing after their boat capsized as they tried to escape by sea to higher ground along the coast.
Mohammed Kamruzzaman, a government magistrate in charge of a Rohingya camp in the Bangladeshi town of Cox's Bazaar, said they used loudspeakers to warn people of the impending danger.
We've also stockpiled dry food, kept medical teams and ambulances on standby and shifted the sick and pregnant women from the camps to hospitals," he said.
Local officials said 113 medical teams had been mobilised to deal with the impact of the cyclone and leave had been cancelled for all government employees.
Experts said Bangladesh was better prepared to handle cyclones than authorities across the border in Rakhine, where tens of thousands of Rohingya made homeless by communal unrest last year languished in flood-prone camps.