France is to invite architects from around the world to submit their designs for a new spire to sit atop a renovated Notre-Dame cathedral.
Prime Minister Edouard Philippe told reporters they hoped for "a new spire that is adapted to the techniques and the challenges of our era".
The spire of the 850-year-old building was completely destroyed in the blaze.
Meanwhile, cathedral bells across France rang out in solidarity with Notre-Dame on Wednesday.
They sounded at 16:50 GMT to mark the exact moment when the blaze started on Monday.
The entire cathedral was only minutes away from total destruction, officials have said.
However, much of the Parisian building - including its famed towers - survived, and thoughts have now turned to how to reconstruct what has been lost.
President Emmanuel Macron vowed it would be rebuilt "even more beautifully", adding that he wanted the work done within five years - although experts warn its reconstruction could take decades.
The spire destroyed in the blaze was added to the cathedral during a 19th Century restoration project led by French architect Eugene Viollet-le-Duc.
Notre-Dame before the fire in 360° video
But Mr Philippe questioned "whether we should even recreate the spire as it was conceived by Viollet-le-Duc... or if, as is often the case in the evolution of heritage, we should endow Notre-Dame with a new spire".
Meanwhile, a copper statue of a cockerel - a symbol of France - that topped the spire has been recovered from the rubble "battered but apparently restorable", the culture ministry said. The cockerel contains holy relics, but it is not yet clear if these are still intact.
Jacques Chanut, president of the French Building Federation, tweeted a picture of the statue being carried by Philippe Villeneuve, the architect in charge of the repair project.
Incroyable! Un de nos adhérents du @GMHistoriques a retrouvé dans les décombres le coq du haut de la flèche de #NotreDame Son intuition était la bonne! Merci à nos bâtisseurs passionnés du patrimoine pour leur engagement: Le savoir-faire français est là. #ReconstruireNotreDame pic.twitter.com/EG2yyj28Bm— Jacques CHANUT (@chanutj) April 16, 2019
So far, €800m ($902m; £692m) has already been pledged by a number of companies and business tycoons to help rebuild the Unesco World Heritage site.
Mr Philippe promised "every euro paid for the construction of Notre-Dame will serve this purpose and nothing else", while also announcing a tax reduction for those donating towards the reconstruction.
On Wednesday, US President Donald Trump said he had spoken to Pope Francis and offered "the help of our great experts on renovation and construction" to rebuild the Roman Catholic cathedral.
Correspondents say it is not yet clear if the Vatican will play any role in repairing the building.
The cause of the fire is unknown but an investigation is under way.
What is the damage?
The blaze, which began on Monday evening and was not fully extinguished until almost 15 hours later, destroyed most of the cathedral's roof and led to the collapse of its famous spire.
Firefighters have used 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 if 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 found 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.
What happens next?
Investigators trying to establish the cause of the fire have begun questioning workers from five companies involved in the renovations that were under way at the cathedral. Officials believe the works could have accidentally led to the disaster.
Offers of help to rebuild the cathedral have come from several world leaders, groups and individuals, including:
- Billionaire François-Henri Pinault, chairman and CEO of the Kering group that owns the Gucci and Yves Saint Laurent fashion brands, who pledged €100m
- Bernard Arnault's family and their company LVMH, a business empire which includes Louis Vuitton and Sephora, who pledged €200m
- French cosmetics giant L'Oreal and its founding Bettencourt family promised to give €200m while oil giant Total pledged €100m
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.
Work to remove the cathedral's paintings will begin on Friday, Mr Riester said.