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An estimated 30,000 Rohingya, a Muslim minority living mostly in Myanmar, have been forced to leave their homes since a bloody crackdown by the army in the western state of Rakhine.
Bangladesh has stepped up patrols on the border to try to stop them from entering, but last week it said thousands had flooded into the country, many with nothing but the clothes they were wearing.
"The situation is fast changing and the actual number could be much higher."
Those interviewed by AFP inside Bangladesh had horrifying stories of gang rape, torture and murder at the hands of Myanmar's security forces.
Analysis of satellite images by Human Rights Watch found hundreds of buildings in Rohingya villages have been razed.
Myanmar has denied allegations of abuse but has also banned foreign journalists and independent investigators from accessing the area to investigate.
Today she vowed to work for "peace and national reconciliation", saying her country faced many challenges, but did not mention the violence in Rakhine state.
"They have been stuck in the island for almost a week without sufficient food and clothes," Abu Ghalib told AFP.
But a spokesman for the Bangladesh border guards said the claims could not be verified as the island was not Bangladeshi territory.
Bangladesh has reinforced its border posts and deployed coast guard ships in an effort to prevent a fresh influx of refugees.
In the past two weeks, Bangladeshi border guards have prevented hundreds of boats packed with Rohingya women and children from entering the country.
But so far little or no aid has been provided for the new arrivals with Bangladeshi authorities fearing food, medicine and shelter will encourage more to cross the border.
Shinji Kubo, who heads the UN refugee agency in Bangladesh, said the new arrivals needed "urgent" help.
"Obviously these people have come from Myanmar after terrible experiences and without any belongings. The winter is approaching. So everyone is really worried about their wellbeing," he said.