The UN has identified more than 35,000 new Rohingya refugees in Bangladesh in the past 24 hours, says a report on BBC.
With this, more than 123,000 Rohingya are now said to have fled violence in Myanmar's Rakhine state since 25 August.
The conflict was triggered by an attack by Rohingya militants on police posts.
This sparked a military counter-offensive that has forced a flood of Rohingya civilians from their villages.
The military says it is fighting against Rohingya militants who are attacking civilians.
Independently verifying the situation on the ground is very difficult because access is restricted, but since the police-post attacks Rohingya families have been streaming north into Bangladesh.
The UN says it is not clear exactly when the latest refugees arrived, but said the number of new arrivals needing food and shelter had surged dramatically.
Two main UN camps for them are now full, so people are sleeping outside or building shelters on open ground and along roads, a spokeswoman said.
Many are in dire need of food and water.
"We fled to a hill when the shooting started. The army set fire to houses," Salim Ullah, a farmer from Myanmar's Kyauk Pan Du village, told Reuters news agency as he arrived in Bangladesh.
"We got on the boat at daybreak. I came with my mother, wife and two children. There were 40 people on a boat, including 25 women."
Fighting appeared to be continuing in Rakhine, a UN situation report said, with smoke seen at least 15 points close to the Bangladesh border.
Thousands of Buddhist villagers in Rakhine are also reported to have fled south. One woman told BBC Burmese she saw Rohingya militants attack people in her village with swords and ran for her life.
The refugee surge comes amid mounting concern in Muslim nations over the plight of the Rohingya.