The UN warning came as it emerged the Dalai Lama had written to Aung San Suu Kyi urging Myanmar's de facto civilian leader to find a peaceful solution to the crisis in the mainly Buddhist country, AFP reported.
The Rohingya, a Muslim minority, have faced decades of persecution in Myanmar where they are regarded as illegal immigrants.
But since the latest upsurge in violence on August 25, hundreds of thousands have flooded across the border into Bangladesh bringing stories of entire villages burned to the ground by Buddhist mobs and Myanmar troops.
On Monday the UN human rights chief Zeid Ra'ad Al Hussein accused Myanmar of waging a "systematic attack" on the Rohingya and warned that "ethnic cleansing" seemed to be under way.
"Because Myanmar has refused access to human rights investigators the current situation cannot yet be fully assessed, but the situation seems a textbook example of ethnic cleansing," he told the UN Human Rights Council.
Suu Kyi, a Nobel peace laureate, has come in for strong international criticism over the military crackdown on the Rohingya, which began when militants ambushed security forces on August 25.
The UN special rapporteur on human rights in Myanmar has said the latest violence may have left more than 1,000 dead, most of them Rohingya.
A further 27,000 ethnic Rakhine Buddhists as well as Hindus have also fled violence that has gripped northern Rakhine, where international aid programs in Rakhine have been severely curtailed.
On Monday it emerged that the Dalai Lama had joined fellow Nobel peace laureates Malala Yousafzai and Archbishop Desmond Tutu in urging Suu Kyi to intervene.
"Questions that are put to me suggest that many people have difficulty reconciling what appears to be happening to Muslims there with Myanmar’s reputation as a Buddhist country," the Tibetan spiritual leader wrote in a letter to Suu Kyi shortly after the latest fighting broke out.
"I appeal to you and your fellow leaders to reach out to all sections of society to try to restore friendly relations throughout the population in a spirit of peace and reconciliation."
The UN refugee agency says at least 313,000 Rohingya have now arrived in Bangladesh from Myanmar's Rakhine state since August 25, around a third of the total population of 1.1 million.
The true figure could be even higher – the UN said many new arrivals are still on the move and are therefore left out of the calculations.
Dhaka initially stepped up border controls after the violence, stranding thousands of refugees at the Bangladeshi frontier, but in the last week has been allowing them to enter.
Refugee camps and makeshift settlements near the border with Myanmar, which already hosted hundreds of thousands of Rohingya before the latest upsurge in violence, are now completely overwhelmed.
That has left tens of thousands of new arrivals with nowhere to shelter from the monsoon rains.
Most have walked for days and the United Nations says many are sick, exhausted and in desperate need of shelter, food and water.
The UN's Zeid said he was "appalled" by reports that Myanmar security forces were laying mines near the border to stop the Rohingya returning.
Three Rohingya are reported to have been killed by a mine, and at least two more have lost limbs. One of the victims was a young boy.
On Sunday the Arakan Rohingya Salvation Army (ARSA) militant group whose attacks sparked the latest crackdown, declared a unilateral ceasefire to allow aid to reach the increasingly desperate refugees.
There was no immediate response from Myanmar's military, but on Saturday authorities said they would set up three relief camps in Rohingya-majority areas.
TRT World Published on Aug 31, 2017 The United Nations says more than 27-thousand Rohingya Muslims have fled to Bangladesh in less than a week. They're escaping from attacks blamed on Rohingya militants, and a crackdown by security forces accused of rights abuses in Rakhine state.