More than 11,000 people crossed into Bangladesh from Myanmar's violence-torn Rakhine State in one day, the United Nations refugee agency said.
Bangladeshi police officer Mohammed Mainuddin told Reuters that 12 bodies - 10 children, one woman and a man - had been recovered.
He said it would be hard for Bangladesh to send back the Rohingya, who have fled the violent "ethnic cleansing" in Rakhine that began once again on August 25, to Myanmar without support from worldwide community.
Officials say over half of the 800,000 refugees flooding out of Myanmar are under 18, and many are making the journey alone.
The foreign minister today alleged that Myanmar is trying to defuse the mounting global pressure by proposing to take back Rohingyas from Bangladesh.
Global aid agencies say some 520,000 Rohingyas have fled to Bangladesh since late August and the United Nations said it was bracing for a possible "further exodus".
It triggered a fresh influx of refugees towards neighboring Bangladesh, though the country sealed off its border to refugees.
On Saturday, Hasina reiterated that the settlements for Rohingya Muslims would be temporary until they returned to their homes in Myanmar.
Among those fleeing were up to 35 people on a boat that capsized off the Bangladesh coast on Sunday.
"We feel deeply sorry for the reaction from global countries based on news without truth".
Those who have fled accuse the military, backed by Buddhist mobs, of using a brutal campaign of killings and village burnings to try to drive them out.
Refugee camps near Bangladesh's border with Myanmar already had about 300,000 Rohingya before the upsurge in violence last month and are now overwhelmed. Their boat had been carrying between 60 and 100 people and was crossing the Bay of Bengal when it capsized.
Authorities have destroyed at least 30 wooden fishing vessels whose captains are accused of smuggling Rohingya and illegal drugs into the country. Villagers, however, say that Rohingya are still attempting to leave and that many are gathered on the beaches just across the water from Bangladesh waiting for a chance to leave the country.
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