Investigators have already begun assessing the damage and questioning people to try to establish what started the blaze that consumed the roof and spire of the 850-year-old Gothic masterpiece.
More then €600m (£518m) has already been raised for rebuilding and restoration and the UK has said it stands ready to help.
Firefighters battled for 14 hours to extinguish the flames, as onlookers feared the entire structure would be wrecked.
But Parisians breathed a sigh of relief when it became clear the twin medieval bell towers had been spared and later when fire investigators revealed that “most precious” treasures have been saved.
They included the Crown of Thorns, a relic venerated by Christians and believed to have been worn by Jesus Christ, as well as the cathedral’s 18th-century organ and a number of artworks.
The fire, which began on Monday evening, is thought to have been caused by an accident rather than arson, the Paris public prosecutor said.
Architects warned repairs could take decades but in a televised address to the nation Mr Macron said: “We will rebuild Notre Dame even more beautifully, and I want it to be completed in five years, we can do it.”
“It is up to us to change this disaster into an opportunity to come together, having deeply reflected on what we have been and what we have to be and become better than we are. It is up to us to find the thread of our national project.”
Pope Francis and the Queen joined global expressions of sorrow for the cathedral.
Vatican spokesman Alessandro Gisotti said the Pontiff called Mr Macron and tweeted: “During the exchange the Holy Father expressed his solidarity with the French people after the blaze that ravaged the Notre Dame cathedral in Paris.”
Notre Dame was undergoing restoration, having been damaged by earlier renovation efforts.
Paris prosecutor Remy Heitz said the inquiry into what caused the fire would be long and complex.
Fifty investigators working on it would interview workers from five companies hired for the renovations to the cathedral’s wooden-beam roof, where the flames first broke out, he said.
A police official said investigators had already questioned nearly 30 people.
Interior minister Christophe Castaner said the structure was now under permanent surveillance because it could still budge.
The hundreds of tons of scaffolding that had been around the spire have heightened the risk from more parts falling.
Notre Dame is part of a Unesco world heritage site and the organisation has offered its expertise in renovations. Poland, the Czech Republic and Greece also offered to send experts.
France’s richest businessman, Bernard Arnault, of luxury goods group LVMH, pledged €200m (£173m) for reconstruction.
Billionaire Francois Pinault and his son, Francois-Henri Pinault, said they were giving €100m (£86m) their company, Artemis, the holding company owning auction house Christie’s and main shareholder of Gucci.
French companies Total and l’Oreal each pledged €100m.
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