The most devastating cyclone to hit France's poorest department in 90 years caused colossal damage in mid-December, killing at least 39 people and injuring more than 5,600.
Authorities have warned the death toll could rise in the archipelago.
The people of Mayotte "often have the sentiment that what we bring them are assurances, pretty words of solidarity", Bayrou said after visiting a desalination plant.
But what they want is "concrete" action, he said.
"After a day of dialogue, we will announce tonight a plan named 'Mayotte standing' that will pave the way," he added.
"And afterwards, there will be a second phase. A long-term plan. Because it's not just about rebuilding Mayotte as it was. It's about designing a different future for Mayotte."
Two weeks after Cyclone Chido, emergency services are still trying to restore water, power and telecoms services.
- Slums -
Estelle Youssouffa, a centrist MP representing Mayotte, said France's aid plan was insufficient to meet the needs of the territory's real population, which includes tens of thousands of undocumented migrants.
Mayotte's population stands officially at 320,000, but there are an estimated 100,000 to 200,000 more clandestine inhabitants living in shanty towns that were utterly destroyed by the cyclone.
The right-wing mayor of the capital, Mamoudzou, who has called for tougher controls on runaway population growth in Mayotte, showed Bayrou the devastated slums covering the hills around the city.
"We can't let people make the same mistakes and hope the outcome will be different," Ambdilwahedou Soumaila told him.
Bayrou arrived with 2.5 tonnes of aid supplies aboard his plane.
He visited a field hospital and a secondary school in a slum that had been looted after the cyclone.
He was accompanied to Mayotte by a large delegation of officials, including Education Minister Elisabeth Borne and Manuel Valls, the new overseas territories minister.
The 73-year-old Bayrou, only recently appointed prime minister, had faced criticism for chairing a local council meeting in his home city of Pau in southern France while Mayotte grappled with the aftermath of the deadly cyclone.
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