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.
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.
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