France will launch an international architectural competition to redesign the roofline of Notre Dame Cathedral after a huge fire gutted the oak-beamed structure and sent its spire crashing into the nave, the prime minister has said.

Édouard Philippe said the competition would give the 850-year-old building “a spire suited to the techniques and challenges of our time”. He said an estimation of the cost of rebuilding the cathedral had yet to be made. French billionaires, multinationals and private citizens have so far raised €880m (£762m) for the restoration.

The French president, Emmanuel Macron, promised the nation on Tuesday night that Notre Dame would be rebuilt – and be “more beautiful than before” – within five years, a timetable many experts consider impossible.

Notre Dame’s rector said he expected the building to remain closed to the public for five to six years. “A segment has been very weakened,” said Bishop Patrick Chauvet.

A fire service spokesman said there was no immediate danger that the structure, which lost two-thirds of its roof in the fire, would collapse. But it was not yet considered secure enough for investigators to enter and start examining the source of the fire in situ, the prosecutor’s office said.

Play Video 1:11 Notre Dame Cathedral: before and after the devastating fire – video

Investigators, who have said they have no reason to believe the blaze was anything but an accident, spoke to about 30 witnesses on Tuesday, including employees of companies involved in a €150m restoration programme that is widely believed to be linked to the fire.

A fire brigade official, Philippe Demay, said the cathedral’s twin towers would have collapsed if the 400 firefighters on the scene had not moved fast and brought in the right heavy equipment. The operation was “extremely difficult”, he said, denying the service could have acted any faster than it did.

On Wednesday evening cathedral bells rang out across France at the exact time the devastating blaze struck on Monday, after the Conference of French Bishops said they would ring nationwide in “solidarity with the diocese of Paris”.

Notre Dame was built over a period of nearly 200 years, starting in the middle of the 12th century, but the lead-covered spire, which reached a height of 93 metres from the ground, was only added in the mid-19th century, during a major restoration project completed by the architect Eugène Viollet-le-Duc.

“The international competition will allow us to ask the question of whether we should even recreate the spire as it was conceived by Viollet-le-Duc,” Philippe told reporters after a cabinet meeting dedicated to the fire.

“Or, as is often the case in the evolution of heritage, whether we should endow Notre Dame with a new spire. This is obviously a huge challenge, a historic responsibility.”

The prime minister said the government would present a bill next week to ensure “transparency and good management” during the reconstruction project, including measures to make sure all donations actually end up going to Notre Dame. Ordinary French citizens will benefit from a tax break of 75% on donations up to €1,000.

Architects have identified three main holes in the structure: where the spire formerly stood, in the transept, and the vault of the north transept. But a Paris fire service spokesman, Gabriel Plus, said on Wednesday the cathedral’s renowned rose windows were in good condition, although there was a risk for the gables in which they were set because these were “no longer supported by the frame”.

Statues inside the gables had been taken down as a precautionary measure to reduce the load on the weakened structure, Plus said. The spire’s bronze rooster, long a symbol of France, was found on Tuesday, deformed by the heat and battered by its fall but nonetheless recognisable.

Facebook Twitter Pinterest Firefighters carrying out safety checks on the cathedral. Photograph: Bastien Louvet/Sipa/Rex/Shutterstock

Many other priceless artefacts inside the cathedral were also saved, including the Crown of Thorns, seen as Notre Dame’s most sacred relic, and the famous 18th-century organ that boasts more than 8,000 pipes. Some paintings and other artworks will be restored at the Louvre after sustaining smoke and water damage.

Stéphane Bern, the government’s culture representative, said on Wednesday that €880m had been raised for the restoration so far, with contributors including Apple, the Total energy group and tycoons who own luxury French brands such as L’Oréal, Chanel, Dior and Louis Vuitton. Many private individuals in France and around the world have also donated.

Experts have said Macron’s five-year timetable, which would see the rebuilding completed by the 2024 Paris Olympics, is highly ambitious. One leading French conservation architect, Pierluigi Pericolo, told French media it was “a colossal task” that would take “no less than 15 years”.

Play Video 0:59 Emmanuel Macron: 'We will rebuild Notre Dame within five years' – video

Pericolo, who worked on the restoration of the 19th-century Nantes basilica, which was badly damaged by fire in 2015, said it could take between two and five years just to check the stability of the weakened edifice. “It’s a fundamental step, and very complex, because it’s difficult to send workers into a monument whose vaulted ceilings are swollen with water,” he told French radio.

“The end of the fire doesn’t mean the edifice is totally saved. The stone can deteriorate when it is exposed to high temperatures and change its mineral composition and fracture inside.”

Companies specialising in the restoration of historic buildings and monuments also warned they would have trouble finding enough skilled workers and apprentices.

“We’ll have to recruit 100 masons, 150 woodworkers and 200 roofers,” said Jean-Claude Bellanger of the artisans’ organisation the Compagnons du Devoir. “The problem is that these manual crafts are undervalued and don’t attract many people. We have the firms and the expertise, but there’s a serious lack of young people for this work.”

Shopkeepers and cafe and restaurant owners in the vicinity of the cathedral have said they too are worried about their futures. Notre Dame receives about 13 million visitors a year, on whom many local businesses depend for their income.

The Île de la Cité on which the cathedral stands is still sealed off and Patrick Lejeune, the president of the local business association, said the group’s 150 members were alarmed. “No one is talking about us,” he said. “I don’t even have access to my office.”

• This article was amended on 18 April 2019 to clarify that the spire reached a height of 93 metres from the ground, not from the roof of the cathedral.