Bangladesh and Myanmar cleaned up on Friday after a killer cyclone wrecked thousands of homes, relieved that the damage was not much worse after the storm weakened as it made landfall.

At least 40 people were either killed by Cyclone Mahasen or while trying to flee its impact, including 25 Muslim Rohingya whose bodies washed up on the shores of Bangladesh after their boat capsized while sailing from Myanmar.

Fifteen people were confirmed as having been killed in Bangladesh by Mahasen, which lashed the southern coast with winds of up to 100 kilometres (62 miles) per hour before being downgraded to a tropical depression.

But there was relief that the toll was not higher, given that cyclones have killed hundreds of thousands of people in both countries in recent decades.

Bangladesh Prime Minister Sheikh Hasina has "expressed gratitude to the Almighty" in Mahasen's aftermath and asked people to "offer thanksgiving prayers", her spokesman Abul Kalam Azad told reporters.

At one stage, up to a million people had taken refuge in makeshift shelters along the Bangladeshi coast, mainly in the densely-populated stretch between the second city of Chittagong and the Cox's Bazaar tourist region.

Most people however have since returned home after the storm passed over, heading towards India as its strength waned.

Hundreds of thousands of people who live in low-lying areas and islands in the vast Meghna river estuary were the most affected, as thousands of their houses were levelled by the cyclone.

"At least 15,000 mud-built houses were damaged by the cyclone in our district," Sirajul Islam, government administrator of Noakhali district, told AFP, adding villagers and fishermen in remote river shoals were the worst hit.

It was a similar picture in Laxmipur district, home to many remote river shoals and islands.

"We've evacuated more than 20,000 people from some islands but most of them are returning home to today," district administrator Mizanur Rahman told AFP.

"We're making a full assessment of the total damages but we know that hundreds of homes were flattened.

"We're also distributing rice to the most affected people."

All 15 of the deaths in Bangladesh were reported in the province of Barisal.

"We're still assessing the damage. We've sent our officials to do surveys. We'll get a full picture by end of today," said provincial commissioner Nurul Amin as he confirmed the toll.

He said an estimated 3,000 mud and tin-roofed houses were flattened by cyclone. "Tens of thousands of trees have fallen on the roads, disrupting communication to some of the worst hit areas."

Bangladesh authorities said the bodies of the Rohingya were found washed up on a beach near the Myanmar border.

"We assume they are of the missing Rohingya" due to their clothing, Cox's Bazaar police chief Mohammad Azad Mia told AFP. Twenty of the bodies were those of children.

Across the border in Myanmar, some 70,000 people were evacuated from villages and camps which are home to large numbers of Rohingya.

However a spokesman for the state government, Win Myaing, said there were no reports of deaths or serious damage.

"There is no more danger from the storm," he said.

He said some of the Rohingya who were evacuated from the camps would return to their tents or shelters, while others would be moved to wooden barracks that the government has been building for them.

"We're working quickly to finish them all by the middle of next month. We're trying to finish them before the rainy season," he said of the new accommodation.

India's meteorological department said Mahasen was now headed over northeastern parts of the country such as Assam, Manipur and Nagaland.

But it is now officially a tropical depression and unlikely to do more than trigger flooding in isolated regions.

burs/co/ia