The exodus figure has jumped about 20,000 in a day and from 164,000 on Thursday. Bangladesh authorities plan to build a camp that could house a quarter of a million people.
"Some 290,000 Rohingya arrived in Bangladesh since August 25," Joseph Tripura, a spokesman for the UN refugee agency, told AFP news agency.
New violence started on August 25 after Rohingya fighters attacked police posts in Rakhine, triggering a security forces crackdown.
Those who have fled across the border have accused the Myanmar military of staging reprisal attacks on Muslim villages.
Officials said the UN has found more Rohingya in Bangladesh villages and areas which were previously not included by relief agencies.
Agencies are now bracing for a new increase in numbers.
Dipayan Bhattacharyya, acting World Food Programme (WFP) head in Bangladesh, told AFP "the situation is very volatile."
"We started with planning for an influx of 120,000. Then we made a resource planning for 300,000. The current influx has almost now reached 300,000." Bhattacharyya said.
Most of the Rohingya are arriving by foot or boat across Bangladesh's 278km border with Myanmar, a fourth of which is made up by the Naf river.
The Rohingya have long been subjected to discrimination in Buddhist-majority Myanmar, which denies them citizenship.
Myanmar's government regards them as illegal migrants from Bangladesh, even if they have lived in the country for generations.
Refugee camps near Bangladesh's border with Myanmar already had about 300,000 Rohingya before the upsurge in violence last month and are now overwhelmed.
Tens of thousands of new arrivals have nowhere to shelter from monsoon rains.
Those flocking into Bangladesh have given harrowing accounts of killings, rape and arson by Myanmar's army. Myanmar authorities deny any wrongdoing.
Most have walked for days and the UN says many are sick, exhausted and in desperate need of shelter.
Source: Al Jazeera and news agencies