PARIS — The ashes have barely settled from the devastating fire that tore through the Notre-Dame cathedral in Paris, but even as France paid tribute on Thursday to the firefighters who saved the structure and its relics, there was a growing debate about how the Gothic landmark should be rebuilt.

Workers are still focused largely on shoring up the damaged structure, but how closely the planned reconstruction should adhere to the original design and materials has become a point of contention in a nation long accustomed to arguing over the balance between modernity and cultural heritage.

President Emmanuel Macron gave the debate particular urgency when he said the cathedral would be rebuilt within five years, a time frame that some experts have called too optimistic. Some of Mr. Macron’s political opponents have even accused him of wanting to rush the restoration in order to have the cathedral ready in time for the 2024 Olympic Games, which will be held in Paris.

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Franck Riester, the French culture minister, said on Thursday that the government would strive to meet the timeline set out by the president, but he also cautioned that rebuilding the cathedral could take more time.