The Rohingya, a stateless 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.
Today 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.
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.
More From This Section
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 programmes in Rakhine have been severely curtailed.
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.
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.