The region has been hit by widespread flooding and devastation affecting Mozambique, Zimbabwe and Malawi.
Mozambique's President Filipe Nyusi called it "a humanitarian disaster of great proportion".
He said more than 1,000 people may have been killed after the cyclone hit the country last week.
Cyclone Idai made landfall near the port city of Beira in Sofala province on Thursday with winds of up to 177 km/h (106 mph).
"This is shaping up to be one of the worst weather-related disasters ever to hit the southern hemisphere," Clare Nullis, from the UN's weather agency, told the BBC on Tuesday.
Christian Lindmeier from the UN's World Health Organization, said: "We need all the logistical support that we can get."
Mozambique's government said 84 people had died and 100,000 needed to be urgently rescued near Beira.
An aerial survey of the province showed that a 50km (30 mile) stretch of land was under water after the Buzi river burst its banks, charity Save The Children said.
The governor of neighbouring Manica province, Manuel Rodrigues, says there is an urgent need to rescue people still trapped, the BBC's Jose Tembe reports.
"It's very sad and very complicated, given what we saw when we flew over the area. We saw people besieged and asking for help," Mr Rodrigues told reporters.
"They were on top of their roofs made up of zinc sheets. Others under flood waters. We saw many people.
"We can only imagine that they had been there for more than two or three days, without food and without clean drinking water."
Nelson Moda was in Beira in Mozambique when the storm hit. He told his story to the BBC OS radio programme:
It was my son's birthday on 14 March and we were all at home.
In the morning this strong storm started and it was moving the city, the trees, and the houses.
It was like a war. It was horrific. The children were crying and we were hiding in the bathroom.
I could see people dying and the house where I live has been destroyed.
There are children who now have no father, no mother, and no home. I saw the city where I grew up being destroyed with my naked eyes.
In Beira, there are no basic services and people don't know what they're going to eat or where they're going to sleep.
I haven't been able to sleep since that night.
In Zimbabwe, the government says 98 people have been killed and more than 200 are missing.
President Emmerson Mnangagwa said that the government was conducting rescue missions and delivering food aid.
In the south-eastern town of Chimanimani residents told harrowing stories of how they lost their relatives when the storm hit.
Some rescuers said homes and even bodies were washed away in the rivers to neighbouring Mozambique, the BBC's Shingai Nyoka reports.