More than 400,000 majority-Muslim Rohingya have fled Myanmar into Bangladesh, the United Nations says as Bangladeshi leader heads to the US to seek global help coping with the crisis.

Bangladesh has been overwhelmed by Rohingya since violence erupted in Buddhist-dominated Myanmar's Rakhine State on August 25.

On Saturday, the UN said that the total number of people to have entered Bangladesh having fled the unrest had now reached 409,000, a leap of 18,000 in a day.

Conditions are worsening in the border town of Cox's Bazar where the influx has added to pressures on Rohingya camps already overwhelmed with 300,000 people from earlier waves of refugees.

The UN said two children and a woman were killed in a "rampage" when a private group handed clothes near a camp on Friday.

Sheikh Hasina, the prime minister of Bangladesh, departed for New York City on Saturday to plead for international help and demand more pressure on Myanmar during talks at the UN General Assembly on Thursday.

"She will seek immediate cessation of violence in Rakhine State in Myanmar and ask the UN secretary-general to send a fact-finding mission to Rakhine," Nazrul Islam, a spokesman for the prime minister, told AFP news agency.

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"She will also call the international community and the UN to put pressure on Myanmar for the repatriation of all the Rohingya refugees to their homeland in Myanmar," he said.

Chris Lom, spokesperson for the International Organisation for Migration (IOM), told Al Jazeera the aid agencies working in the country were struggling to cope with the demand.

"Nobody expected this number of people. Of course, if 100,000 would have come, they could have been accommodated, but by the time they stop, it may be 500,000 and may be more. It's huge," he said.

Lom said aid agencies were working "as fast as they can" but had so far been able to assist less than a quarter of the refugees.

'Ethnic cleansing'

Foreign Minister AH Mahmood Ali said: "We will continue international pressure on the Myanmar government to immediately end its ongoing ethnic cleansing of the Rohingya."

The foreign ministry on Friday summoned the Myanmar charge d'affaires for the third time in Dhaka to protest at alleged violations of its airspace by Myanmar drones and helicopter.

The ministry warned that the three violations between September 10 and 14 could lead to "unwarranted consequences". Myanmar did not immediately comment.

The Bangladesh government earlier protested to the embassy over the planting of landmines near their border, which have killed several Rohingya, as well as over the treatment of the refugees.