The number of those crossing the border into Bangladesh - 87,000, based on calculations by United Nations workers - surpasses the number who escaped Myanmar after much smaller insurgent attacks in October last year set off a military operation.
Bangladesh officials have said at least 54 people have drowned trying to reach the country.
"No non-government organisations came here. We have no food. Some women gave birth on the roadside. Sick children have no treatment," said Mr Mohammed Hussein yesterday. The 25-year-old was still looking for a place to stay, four days after fleeing.
Most of the new arrivals have crammed into camps near the border, where the UN said local people were helping the relief effort.
Among new arrivals, about 16,000 are school-age children and more than 5,000 are under the age of five who need vaccine coverage, aid workers said over the weekend. The number of unaccompanied children is high and many are "traumatised and hungry", they said.
The UN special rapporteur for human rights in Myanmar, Ms Yanghee Lee, has criticised Ms Suu Kyi for failing to protect the Rohingya.
"The de facto leader needs to step in - that is what we would expect from any government, to protect everybody within their own jurisdiction," said Ms Lee.
Protests have broken out in Malaysia, Indonesia, Turkey and the Russian region of Chechnya over the Rohingya's plight, as anger grows among Muslims about violence against the group.