An overcrowded boat ferrying Rohingya refugees from Myanmar capsized Tuesday off the coast of Bangladesh, police said, killing at least four people on board.

Police said the vessel sank in rough weather as it approached the coast near Shamlapur village, where thousands of Rohingya refugees fleeing violence in Myanmar have arrived by boat since August.

"There were at least 33 people in the small trawler, which capsized after it was caught in high waves and bad weather," local police chief Abul Khair told AFP.

He said one person was found dead at the scene while six others were rushed to hospital in a critical condition, where three later died.

The rest were dragged ashore or managed to swim to safety, Khair added.

He said the victims were all Rohingya from Buthidaung district in Myanmar's westernmost Rakhine State, from where more than 600,000 of the persecuted Muslim minority have fled since August 25.

Most have crossed by land into neighbouring Bangladesh, where refugee camps have been overwhelmed by sick and injured civilians fleeing violence.

But others have made the dangerous voyage by sea, taking rickety fishing boats into the Bay of Bengal and snaking up the coastline of Bangladesh looking for a spot to make landfall.

At least 200 have drowned on this treacherous sea route since August.

The United Nations says an estimated 605,000 Rohingya had arrived in Bangladesh since late August fleeing an upsurge in ethnic violence in Rakhine State.

Those displaced inside Bangladesh have described systematic massacres, rapes and arson in their villages by Myanmar troops that the UN has likened to a campaign of ethnic cleansing.

Source: AFP