"UNHCR is gravely concerned about the continuing conflict in Myanmar and by reports that civilians have died trying to seek safety," the UN refugee agency said in a statement.
Thousands of people, including women and children, were streaming across the border into southeast Bangladesh after walking for days through forests, rice paddies and jungles to reach safety and were now crowded into existing camps and sheltering at makeshift sites.
Several thousand people were believed to have drowned trying to cross the river that separates Myanmar from Bangladesh.
Many are in dire need of food and water.
"Those who have made it to Bangladesh are in poor condition... They are hungry, weak and sick," said UNHCR.
"An unknown number could still be stranded at the border," UNHCR warned.
Separately, the UN migration agency the International Organisation for Migration said on Tuesday that it and partner agencies operating in the area were appealing for $18 million to help the refugees over the next three months.
More than 30,000 Rohingya are estimated to have sought shelter in the existing refugee camps of Kutupalong and Nayapara, which are "at breaking point", the agency stated.
Other Rohingyas are being hosted by refugee families and in refugee schools, community centres, Islamic schools and other buildings, said UNHCR. "We are running out of available space," the agency said.
UNHCR said it was working with local authorities and an NGO partner to provide essential items for the refugees including clothes, plastic sheets and sleeping mats.
"There is an urgent need for additional emergency shelters and land as more refugees arrive," UNCHR said.
UNHCR urged Bangladesh's authorities to allow safe passage to those fleeing violence and to register and document all refugees arriving in the country to help the UN and charities get aid to where it is needed.
"We are also identifying vulnerable arrivals, including unaccompanied children, who need additional care and protection," said UNHCR.
The latest influx of Rohingya began on August 25 when Rohingya insurgents attacked Myanmar police security posts, prompting security forces to launch a counter-offensive.
Myanmar security officials and Rohingya insurgents accuse each other of committing atrocities and witnesses have also reported these being carried out by Buddhist mobs.
Thousands of Buddhist villagers in Mayanmar's Rakhine state are also reported to have fled south.
Independently verifying the situation on the ground is hard because access is restricted.
The Rohingya are a stateless mostly Muslim ethnic minority who have long faced persecution in Rakhine state. Bloody riots in 2012 forced over 100,000 to flee to refugee camps in Bangladesh, where many still live.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
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Doraiah Chowdary Vundavally is a Software engineer at VTech . He is the news editor of SocialNews.XYZ and Freelance writer-contributes Telugu and English Columns on Films, Politics, and Gossips. He is the primary contributor for South Cinema Section of SocialNews.XYZ. His mission is to help to develop SocialNews.XYZ into a News website that has no bias or judgement towards any.