(CNN) Rohingya refugees who have fled violence in Myanmar for shelter in neighboring Bangladesh are in desperate need of help, UN refugee chief Filippo Grandi said Wednesday, as he called on the Myanmar authorities to halt the violence.

Grandi, who returned Tuesday night from a trip to Bangladesh, said he had rarely seen people who had left their homes with so little.

"They have absolutely nothing," he said. "Evidently they had to flee from a very urgent situation, from very sudden violence -- so they need everything," he said.

Who are the Rohingya and why are they fleeing?

Who are the Rohingya and why are they fleeing? 02:30

Who are the Rohingya and why are they fleeing?

According to the latest report from the Inter Sector Coordination Group (ISCG) in Bangladesh, at least 480,000 Rohingya refugees have arrived in Bangladesh since clashes began on August 25.

Grandi, the UN High Commissioner for Refugees, said that including some 300,000 Rohingya refugees already in Bangladesh, between 700,000 and 800,000 people were now sheltering there in overcrowded and insanitary conditions, posing a risk of epidemics.

On top of that, he warned that "the risk of the spread of terrorist violence in the whole region is very, very high" if the situation is not resolved.

"It is very clear that the cause of this crisis is in Myanmar, but the solution of this crisis also lies in Myanmar," he said.

"Let me once again, as many other colleagues have done, as the (UN) secretary-general has done, let me reiterate the urgent call to the authorities in Myanmar to stop violence, for violence to stop in Rakhine State, in northern Rakhine State, and when that happens, and conditions stabilize, we have to start thinking about solutions."

The Myanmar authorities have said the violence in Rakhine State was instigated by Rohingya militants and deny UN accusations of " ethnic cleansing ."

Grandi, who visited Rakhine State in July, condemned the insurgent attacks that left 12 police officers dead the following month. But he stressed that underdevelopment in Rakhine state -- and particularly the poor treatment of the Rohingya Muslims -- had played a large part in the current crisis.

"It was ... very obvious to me when I visited northern Rakhine that it was just a matter of time before terrorism would spring up from the situation of discrimination or poverty that prevailed in that area," he said.

"The terrain is very fertile for that, so it is also a question of addressing this issue not only for the Rohingya, not only for northern Rakhine, but for the entire region. Because if the situation is not resolved, the risk of the spread of terrorist violence in the whole region -- and this is a particularly fragile region -- is very, very high."

Grandi added that the "big question" was whether the Rohingya refugees would be able to return to Rakhine state.

He called on the Myanmar authorities to implement the recommendations of a UN advisory panel headed by former UN chief Kofi Annan. Two key points were the lack of citizenship for Rohingya in Myanmar and the "dramatic underdevelopment" of Rakhine state, affecting both Buddhist and Muslim communities, he said.

Grandi said he hoped to discuss the issue of Rohingya statelessness with Myanmar authorities at a meeting in Geneva, Switzerland, next week.

JUST WATCHED Who is Aung San Suu Kyi? Replay More Videos ... MUST WATCH Who is Aung San Suu Kyi? 01:41

Grandi praised the response of the Bangladeshi government to the sudden influx of refugees and said aid efforts were now making headway after a "chaotic" start.

But he warned that healing the great trauma he had witnessed among women and children in the refugee camps would be far harder than meeting their physical needs, great though they were.

Women had been raped or fought off attackers, he said, and many children had witnessed the killing of their parents, relatives or friends.