According to Cyclocane, Idai is now over both Mozambique and Zimbabwe, and is travelling northwest.
According to officials on Monday, the scale of destruction is only becoming apparent as rescuers reached the most affected areas near the border with Mozambique.
Nyusi spoke after flying by helicopter over the Indian Ocean port city of Beira and the rural Manica and Sofala provinces, where he reported widespread devastation.
"Waters from the rivers Pungue and Buzi have broken their banks, wiping out entire villages, isolating communities and we could see, as we flew above, bodies floating", the Mozambican President said. "A real disaster of great proportions".
With Beira's airport closed, the Red Cross team drove from Mozambique's capital Maputo before taking a helicopter for the last part of the journey because roads into Beira have been flooded.
The destruction there is "massive and horrifying", said Jamie LeSueur.
It made landfall on Thursday with winds of up to 177 km/h (106 mph), but aid teams only reached Beira on Sunday.
"The situation is awful".
The IFRC warned that the death toll could rise once the full scale of the devastation is known, and that further heavy rain is expected.
The Red Cross said 90 percent of the city was damaged or destroyed.More news: New Zealand PM Ardern vows never to speak killer's name
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Manicaland Province was worst hit in Zimbabwe, with severe flooding prompting a nationwide state of emergency.
Four days have passed since Cyclone Idai barreled into the coast of southeastern Africa, and the extent of the damage is only now becoming clearer.
"Almost everything is destroyed", LeSueur added.
A $50 million rescue and rebuild mission is now underway to fix roads, bridges, schools, communication lines and provide healthcare to those affected.
Beira has been severely battered by the cyclone which cut off electricity, forced the airport to shut down and cut off road access to the rest of the country. "We have people now suffering, some on top of trees and are badly in need of help". Communication out of the city has been slow, with telephone lines knocked out.
People carry their personal effects after Tropical Cyclone Idai, in Beira, Mozambique.
At least 68 people have died in Mozambique, mostly around Beira, the authorities there say.
Zimbabwe government spokesman Nick Mangwana told AFP that the death toll in the country was "is now at 39".
Speaking on the destruction caused by the cyclone, Mozambique's President Filipe Nyusi said the damage is "very worrisome" and said that the flooding made it hard for aircraft to land and carry out rescue operations, according to Mozambique's state radio.
The Zimbabwe Information Ministry shared pictures of some pupils who had been rescued from a boarding school in Chimanimani District, one of the worst-affected areas in the east of the country.