But not all those going on the ill-equipped trawlers or fishing boats are Rohingya refugees.
The Rakhine Buddhists and Muslims, believed to be mainly Rohingya, blame each other for the violence.
One official said 52 Rohingya had been sent back in the last few days.
Malaysia has allowed the United Nations Refugee Agency to assess Rohingya claims for asylum.
There are also immediate concerns for about 126 Rohingya thought to be in Thai custody.
Bangladesh says the Rohingya have been living in Myanmar for centuries and should be recognized there as citizens.
Other boatloads of Rohingya have allegedly been set adrift after being towed out to sea by Thai authorities.
The Bangladesh border guards said they had sent back more than 1, 000 Rohingya Muslims in the past several days.
It is believed to be one of the largest groups of Rohingya migrants to have arrived in Malaysia this year.
There were reports of another boatload of 46 Rohingya detained by the Thai military Friday, but there was no official confirmation.
Officials said their clothing suggested they were bodies of Muslim Rohingya missing since their boat capsized off the coast of western Burma on Monday.
Ahead of its arrival, UN agencies had warned that tens of thousands of Rohingya Muslims displaced by ethnic violence last year were at risk.
In the past, Rohingya refugees caught in Thailand were handed over to the immigration authorities, says Chris Lewa, a longtime advocate for Rohingya rights.
The head of the Association of Southeast Asian Nations, a grouping that includes Myanmar, has warned that the Rohingya crisis could destabilise the region.
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The U.N. estimates the Rohingya population in Myanmar at 800, 000 people.
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"We are very worried about the cyclone... we do not have enough food to eat, " a member of the Rohingya community told Agence-France Presse news agency.
Kiswanto said 25 Rohingya asylum seekers were being questioned by police and would be prosecuted under Indonesia law if suspected of being involved in the killings.
There have been influxes of Rohingya before and in 2009 the Thai government was heavily criticised for its policy of towing boats back out to sea.
Boatloads of Rohingya arriving in Thailand is nothing new, but non-governmental organizations are increasingly worried about what they say is an apparent change of government policy.
Thai senators began looking into claims that troops operating on an island off the country's coast are detaining Rohingya refugees from Myanmar and setting them out to sea.
Bangladeshi officials estimate 300, 000 Rohingya Muslims live in the country, with about a tenth of them in two official refugee camps in the southern district of Cox's Bazaar.
The United Nations High Commissioner for Refugees says it is "concerned" about the fate of the Muslim ethnic minority Rohingya people, who have fled from Myanmar's border with Bangladesh.
Nosima, a 19-year-old Rohingya, says that after four years in Bangladesh the local MP in the border district of Bandarban sent her family and a few others back to Myanmar.
Lucy Hocking's was joined on BBC World News by Baroness Cox, the founder of the Humanitarian Aid Relief Trust charity and by Nurul Islam, of the Arakan Rohingya National Organisation.
BBC: Burma's Rohingya: Aung San Suu Kyi surprisingly 'quiet'
In January, when his government was under pressure over the army's callous treatment of ethnic-Rohingya boat people, originally from Myanmar, Abhisit Vejjajiva, the prime minister, told journalists that the illegal-immigrant problem had to be solved.
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