Wild elephants trampled two elderly Rohingya refugees to death yesterday as they slept underneath a plastic sheet near a forest in Bangladesh, police said.

The incident occurred on the outskirts of Kutupalong refugee camp in Cox's Bazar district, where tens of thousands of Rohingya have set up makeshift shelters since fleeing violence across the border in Myanmar.

"We can confirm that two people were killed by wild elephants," local police chief Abul Khaer told AFP, adding both the deceased were Rohingya civilians.

Space at established refugee camps in Bangladesh has all but been exhausted, with new arrivals hacking away trees and other vegetation anywhere they can to erect shelters from the monsoon rain.

Many newly-arrived refugees are camping in the open or along roadsides, where they rush aid trucks for food and other desperately needed supplies.

Rohingya elder Kamal Hossain said the two refugees killed by elephants were new arrivals, who had taken refuge in a forested area near the sprawling Kutupalong camp.

"It happened early Monday morning when the Rohingya were sleeping under plastic tents. The wild elephants trampled the two elderly civilians to death," Hossain told AFP.

Many of the displaced have arrived with horrific tales of killings and rapes by Myanmar's security forces and Buddhist militias.