French President Emmanuel Macron says Notre-Dame cathedral will be rebuilt "even more beautifully" - and that he wants the work done within five years.
A massive fire on Monday ravaged the 850-year-old Gothic building, destroying much of its roof and causing its steeple to collapse.
The cathedral was minutes away from total destruction, officials say.
But despite Mr Macron's pledge experts say its reconstruction could take decades.
Fifty people will investigate the cause of the fire. Paris public prosecutor Rémy Heitz said there was no obvious indication of arson and that the blaze was being treated as an accident.
A combined €800m ($902m; £692m) has already been pledged by a number of companies and business tycoons to help rebuild the Unesco World Heritage site.
What has Macron said?
In a televised address on Tuesday evening, President Macron suggested he wants it rebuilt by the time Paris hosts the Summer Olympics in 2024.
"We'll rebuild Notre-Dame even more beautifully and I want it to be completed in five years, we can do it," said Mr Macron, who had already pledged to launch an international fundraising scheme for the reconstruction.
"It's up to us to convert this disaster into an opportunity to come together... It's up to us to find the thread of our national project."
But Eric Fischer, head of the foundation in charge of restoring the 1,000-year-old Strasbourg cathedral, told AFP the Notre-Dame may take "decades" to rebuild.
Frédéric Létoffé, the head of the group of companies for the Restoration of Historic Monuments, put the timescale at between 10 and 15 years, warning substantial work would be needed to secure the site before restoration can begin.
What is the damage?
The blaze - which was discovered at 18:43 (16:43 GMT) on Monday and was fully extinguished almost 15 hours later - destroyed most of the cathedral's roof and led to the collapse of its iconic spire.
Experts have not yet been allowed on site to assess the damage and firefighters have sent a drone to survey the scale of the destruction.
Photos appear to show that at least one of the famed rose windows has survived but there are concerns for some of the other stained-glass windows. The 18th Century organ has not been burned but it is not clear whether it is damaged.
It was still too early to estimate the cost of the damage, said the Fondation du Patrimoine, an independent non-profit heritage group.
Deputy Interior Minister Laurent Nuñez said the structure was in good condition "overall" but that "some vulnerabilities" had been identified in the stone vaults and the remainder of the ceiling.
The main structure, including the two bell towers, was saved in a time window of 15 to 30 minutes by a team of 400 firefighters, he said.
In his speech Mr Macron heaped praise on the fire services, saying they took "extreme risks" to tackle the blaze.
Praying for the cathedral
They sit or stand in a crowd, many of them young people, spilling over the end of the Boulevard Saint Michel, this first evening after the fire, singing hymns. On a table beneath the towering sculpture of Saint Michael stands a statue of Our Lady - Notre Dame.
"As a French Catholic," says Éloi, 22, "I felt really bad after the fire so I see this vigil as a way to say that even if the flames destroyed the cathedral, we can rebuild it because the Church is made not of stones but is a living body." He believes the cathedral should be remade just the way it was, as a "prayer to God".
"We are Catholics," he adds, "but all French people - Catholics, Muslims, atheists - are united around this disaster and in the hope it will be rebuilt."
And they are united in pride in the fire brigade. During the concert, an engine hurtles past on the road, and the singing stops as the crowd claps and cheers.
What happens next?
Investigators trying to establish the cause of the fire have begun questioning workers from five companies involved in the extensive renovations that were under way at the cathedral. Officials believe the works could be linked to the disaster.
"Nothing indicates this was a deliberate act," said public prosecutor Rémy Heitz, adding that he expected to be a "long and complex" case.
Offers of help to rebuild the cathedral have come from several world leaders, groups and individuals, including:
Culture Minister Franck Riester said some of the artwork and religious items rescued would be sent to the Louvre museum where they would be kept and eventually restored.
They include what is said to be the crown of thorns worn by Jesus before his crucifixion and a tunic King Louis IX is said to have worn when he brought the crown to Paris.
The cathedral's paintings would be removed from Friday, Mr Riester said.