As many as 40,000 Rohingya Muslims have fled Myanmar in the last week, since violence flared between Rohingya fighters and government soldiers in the Rakhine state.
According to UN officials in neighbouring Bangladesh, an estimated 38,000 people have crossed the border into the country, with reports that fleeing civilians were being shot at.
UNHCR regional spokeswoman Vivian Tan told the BBC that they are "seeing lots of makeshifts tents and shelters on the side of the road - every available space is being occupied".
The latest figures come as Burma’s military claimed to have killed almost 400 insurgents in the fighting. Reports also emerged of corpses of Rohingya women and children washing up on the riverbanks in Bangladesh. Myanmar’s government claims just 29 civilians have been killed.
Chris Lewa of the Arakan Project advocacy group said fleeing civilians had reported massacres committed by the Burmese military. “We were told that the army encircled the village and attacked people when they fled,” he said.
The violence flared after fighters from the Arakan Rohingya Salvation Army (ARSA) launched coordinated attacks against police posts in the Rakhine state, and attempted to break into an army base earlier this week.
Burmese leader Aung San Suu Kyi labeled the offensive a "terrorist" attack that was "a calculated attempt to undermine the efforts of those seeking to build peace and harmony in Rakhine state".
On Thursday the UN Special Rapporteur on human rights in Myanmar, Yanghee Lee, said the "worsening cycle of violence" was of "grave concern and must be broken urgently".
US Ambassador to the UN Nikki Haley also said that Myanmar’s security forces had "a responsibility to adhere to international humanitarian law, which includes refraining from attacking innocent civilians and humanitarian workers and ensuring assistance reaches those in need".