Defending his initial remarks, Bieuville insisted “I have never been alarmist, I was simply unable to give the number of victims”.
Officials said it had been difficult to determine the scale of fatalities in the wake of the disaster 10 days ago, due to many areas of Mayotte being inaccessible and the fact that victims were buried within 24 hours in accordance with Islamic customs.
There is also uncertainty about the true population of Mayotte, a French Indian Ocean territory.
Officially it has 320,000 residents, but authorities estimate about 100,000 to 200,000 undocumented migrants may also be living there.
“I think [the number of dead] will be in the dozens and not in the thousands,” the prime minister told BFMTV on Monday night.
The archipelago is one of the poorest parts of France, with many of its residents living in shanty towns.
Cyclone Chido was the worst storm to hit the territory in 90 years, bringing winds of up to 260 km/h (160mph) and flattening areas where people lived in shacks with metal roofs.
France held a day of national mourning in the wake of the cyclone on Monday. President Emmanuel Macron visited the territory last week, and was heckled by angry locals demanding more aid in devastated areas.
Some survivors went for a week without water, communication or electricity.
Authorities restored water in the main points of the territory on Tuesday, Bieuville said. “Even if this water is still sometimes a little difficult to deliver, our fellow citizens have water.”
He also said there was no fuel shortage any more and cars could now be filled up.
The prime minister had earlier said that a field hospital would also be operational by Tuesday morning.
Cyclone Chido moved on to continental Africa after hitting Mayotte, killing 120 people in Mozambique and 13 in Malawi.