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 (Thursday NZT).
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.
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.
So far, €800 million ($NZ1.3 billion) 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.