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

At least 48 people were either killed by Cyclone Mahasen or while trying to flee its impact, including 31 Muslim Rohingya whose bodies washed up on the shores of Bangladesh after their boat capsized while sailing from Myanmar.

Seventeen 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 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.

Nearly 94,000 mud, straw and tin-built houses were completely or partially damaged by the cyclone in the country's coastal districts, according to a provisional government estimate.

"Of the total, 49,000 houses were completely destroyed and 45,000 houses were partly damaged," the government's disaster management spokesman Abdul Wazed told AFP.

"Crops on a large swathe of land were also damaged," he said, adding the authorities had dispatched relief items to the coastal districts. "We're also distributing rice to the most affected people."

He said a final estimate of the damage would be known by next week.

"We're still assessing the damage. We've sent our officials to do surveys in all the remote islands and areas. We'll get a full picture very soon," Nurul Amin, commissioner of the worst-affected Barisal province, told AFP.

"Tens of thousands of trees have fallen on the roads, disrupting communication to some of the worst-hit areas."

Bangladesh authorities said 31 bodies of Rohingya were found washed up on a beach near the Myanmar border, including 25 children and six women.

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.

The International Organization for Migration, which has joined the damage assessment teams, said the preparations by both countries' governments had prevented a much higher toll.

"If this same storm had hit 20 years ago, we might have seen thousands of deaths. As it is, people are already leaving the storm shelters to go home," he added," said Brian Kelly, the IOM's Asia-Pacific emergency advisor.

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.