Thousands have moved to shelters in Bangladesh but in Burma, authorities have encountered a deep reluctance to move among Rohingya refugees |
The Bangladeshi authorities have raised the danger level to seven out of 10 for low-lying areas around Chittagong and the coastal district of Cox's Bazar.
In Burma, some displaced people have resisted calls for them to evacuate camps in Rakhine state.
It is predicted that the cyclone will make landfall on Thursday.
The United Nations has warned that 8.2m people could be at risk from Mahasen in Bangladesh, Burma and north-east India.
Tens of thousands of Rohingya Muslims living in camps in low-lying areas of Burma's Rakhine state are feared to be at risk.
They were displaced by ethnic violence last year and many are reluctant to move from the camps.
Hla Maung said he lost his mother and two young daughters during the clashes between Muslims and Buddhists.
"I lost everything. I don't want to go anywhere. I'll stay here. If I die, I want to die here," he said.
Rakhine state said it had moved some 36,000 displaced people from camps, Kirsten Mildren, from the UN Office for the Co-ordination of Humanitarian Affairs (Ocha), told the BBC.
But she said the evacuation was "not moving as fast as we'd like - it's certainly a race against time. We're finding it very difficult to convince [people] to move to higher ground or safer buildings."
Burmese planning minister Tin Naing Thein claimed that in all more than 166,000 people had been relocated, but there was little evidence of a mass evacuation in reports from the affected area.
Correspondents say the Burmese evacuations are seen as a test of the government's resolve to assist the Rohingya, amid allegations that state forces stood by or even participated in last year's anti-Muslim violence.
On Tuesday, President Thein Sein was quoted as urging officials to "carry out relief work on humanitarian grounds for all, regardless of race and religion", at a meeting to co-ordinate relief efforts for Cyclone Mahasen.
In Bangladesh, hundreds of thousands of people inhabiting areas just a few metres above sea level were being moved on Wednesday ahead of a feared storm surge of 5m (16 feet) or above.
Airports in Cox's Bazar and Chittagong have been shut until the danger subsides.
Though the storm did not make landfall in Sri Lanka, the associated heavy rain caused floods and mudslides which killed at least seven people, according to the country's Disaster Management Centre.
At least 50 Rohingya Muslims were feared drowned on Tuesday when boats evacuating them from the path of the cyclone capsized off western Burma.
More than 100,000 people died in 2008 when Cyclone Nargis devastated many of Burma's coastal villages.
Credit & Copy From; http://www.bbc.co.uk/news/world-asia-22537615