The figure has jumped about 20,000 in a day.
"Some 290,000 Rohingya arrived in Bangladesh since August 25," said Joseph Tripura, a spokesman for the UN refugee agency.
Officials said the UN has found more Rohingya in villages and areas which were previously not included by relief agencies.
Most of the Rohingya are arriving by foot or boat across Bangladesh's 278 kilometre (172 mile) border with Myanmar, a fourth of which is made up by the Naf river.
On Thursday the UN had put the number at 164,000.
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 and are now overwhelmed.
The 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. The Myanmar authorities deny any wrongdoing.
Most have walked for days and the United Nations says many are sick, exhausted and in desperate need of shelter, food and water.
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