The United Nations has warned that more than eight million people could be at risk from Cyclone Mahasen, which is expected to make landfall tomorrow or Friday somewhere near the border between the two countries.
Bangladesh told hundreds of thousands of people living in low-lying areas to move to cyclone shelters, while Myanmar announced plans to move roughly 166,000 people at risk on its northwest coast.
"The military will move them to higher ground" and to emergency shelters in schools, Aung Min, minister of the Myanmar president's office, said at a news conference in Yangon.
The cyclone appeared to have lost some of its strength as it churned northwards through the Bay of Bengal, the UN Office for the Coordination of Humanitarian Affairs (OCHA) said in a statement released late Tuesday.
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But it may still bring "life-threatening conditions" for 8.2 million people in northeast India, Bangladesh and Myanmar, it warned, adding Bangladesh's Chittagong and Cox's Bazaar areas could face the worst of a tidal surge and heavy rains.
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.