"For the moment we have registered 84 deaths officially, but when we flew over the area ... this morning to understand what's going on, everything indicates that we could register more than 1,000 deaths", Nyusi said, reported Qatar-backed Al Jazeera TV.
The Red Cross said 90 percent of the city was damaged or destroyed.
More than a thousand people are feared to have died in a cyclone that smashed into Mozambique, while scores have been killed and more than 150 are missing in neighbouring Zimbabwe.
He called the situation a "real humanitarian disaster of large proportions".
The cyclone comes a week after severe flooding had affected 1.5 million people in Mozambique and Malawi, killing at least 120 people in both countries, United Nations officials said. "The scale of devastation is enormous", said Jamie LeSueur, who is leading IFRC's assessment team, in an IRFC statement.
Satellite imagery shows that Malawi's Chikwawa district has been particularly badly affected by flooding, while Mozambique's Zambezia and Tete provinces have also seen tens-of-thousands displaced and more than 168,000 hectares of crops reportedly affected.
As the cyclone approached, the Red Cross sent out more than 200 volunteers to areas most likely to be affected. Mr. Sacco said the death toll was expected to rise as authorities continued to assess the situation.
Inhabitants of Chiluvi, a village in central Mozambique, walk last week along a flooded and muddy street after Cyclone Idai and floods that hit the region.
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"Beira global airport had been shut after the air traffic control tower and navigation equipment were destroyed by the cyclone".
Beira is home to a major port that is essential for the supply of goods to the central part of the country, as well as Zimbabwe and Malawi, which are landlocked.
More than 80 people have died in eastern and southern Zimbabwe, information ministry head Nick Mangwana told Reuters news agency.
A major aid operation is under way in Mozambique and Malawi to help victims of Tropical Cyclone Idai, which has reached the densely-populated Mozambican port city of Beira, after registering maximum wind speeds of almost 200 kilometres per hour. Air force helicopters began carrying injured people to hospitals after the weather improved later on Sunday.
Local people in Beira, with a population of 500,000, have put in an "incredible effort" to reopen roads in the city, Mr LeSeur told the BBC's Newsday programme.
Aerial view of Tengani, Nsanje, Malawi, affected by floods due to the incessant rains from March 5 to March 9 2019.