(Corrects figure to 700 million euros, not billion, in paragraph 21)
* Public prosecutor says no sign of arson
* Billionaires, companies pledge donations for rebuild
* 3D diagram of Notre-Dame: tmsnrt.rs/2DgH76t
* Map and timeline: tmsnrt.rs/2DgHcXP
By Richard Lough and Elizabeth Pineau
PARIS, April 16 (Reuters) - Parisians gave thanks to see the bell towers and great stained-glass rose window of Notre-Dame still standing on Tuesday, after firefighters laboured through the night to douse the flames that gutted one of the most potent national symbols of France.
Authorities said they suspected the fire was caused by accident. President Emmanuel Macron declared that the cathedral would be rebuilt. Industrialists pledged hundreds of millions of euros. Ordinary people sang, wept and prayed below the cathedral that has towered above the capital for more than 800 years.
More than 400 firemen were needed to tame the inferno that consumed the roof and collapsed the spire of the gothic masterpiece. They worked through the night, finally quelling the blaze some 14 hours after it began.
"Yesterday we thought the whole cathedral would collapse. Yet this morning she is still standing, valiant, despite everything," said Sister Marie Aimee, a nun who had hurried to a nearby church to pray as the flames spread.
"It is a sign of hope."
From the outside, the imposing bell towers and outer walls, with their vast buttresses, stood firm, though the insides and the upper structure had been eviscerated.
Paris public prosecutor Remy Heitz said there was no obvious indication the fire was arson. Fifty people were working on what would be a long and complex investigation, officials said.
One firefighter was injured but no one else was hurt, with the fire starting at around 6.30 p.m. after the building was closed to the public for the evening.
Firefighters examined the facade, with its spectacular 10-metre filigreed stained-glass rose window still intact. They could be seen walking atop the belfries as police kept the area in lockdown.
Investigators will not be able to enter the cathedral's blackened nave until experts are satisfied its walls withstood the heat and the building is structurally sound.
The fire swiftly ripped through the cathedral's oak roof supports, where workmen had been carrying out extensive renovations to the spire's timber-framed supports.
The Paris prosecutor has opened an investigation into "involuntary destruction by fire". Police on Tuesday began questioning the workers involved in the restoration, the prosecutor's office said.
Hundreds of stunned onlookers had lined the banks of the river Seine late into the night, reciting prayers and singing as they stood in vigil while the fire raged.
It was at Notre-Dame that Henry VI of England was crowned "King of France" in 1431, that Napoleon was made emperor in 1804, and Pope Pius X beatified Joan of Arc in 1909. Presidents Charles de Gaulle and Francois Mitterrand were mourned there.
Messages of condolence flooded in from around the world.
Pope Francis, the leader of the Catholic Church, was praying for those affected, the Vatican said, adding: "Notre-Dame will always remain - and we have seen this in these hours - a place where believers and non-believers can come together in the most dramatic moments of French history."
Britain's Queen Elizabeth expressed deep sadness while her son and heir Prince Charles said he was "utterly heartbroken". Chancellor Angela Merkel offered German help to rebuild a part of "our common European heritage".
Considered among the finest examples of European Gothic architecture, Notre-Dame is visited by more than 13 million people a year. It sits on an island in the Seine, overlooking the Left Bank hangouts of Ernest Hemingway and Pablo Picasso.
"Notre-Dame de Paris is the cathedral of the people, of the people of Paris, of the French people, of the people of the world. It is part of those references of our history, of what we have in common, of what we share," said Interior Minister Christophe Castaner.
The cathedral is owned by the state and has been at the centre of a years-long row between the nation and the Paris archdiocese over who should finance restoration work to collapsed balustrades, crumbling gargoyles and cracked facades.
Within 24 hours, companies and local authorities had pledged more than 700 million euros to rebuild it, including 500 million from the three billionaire families that own France's giant luxury goods empires: Kering, LVMH and L'Oreal.
It was too early to estimate the cost of the damage, said the heritage charity Fondation du Patrimoine.
Paolo Violini, a restoration specialist for Vatican museums, said the pace at which the fire spread through the cathedral had been stunning.
"We are used to thinking about them as eternal simply because they have been there for centuries, or a thousand years, but the reality is they are very fragile," Violini said.
The company carrying out the renovation works when the blaze broke out said it would cooperate fully with the investigation.
"All I can tell you is that at the moment the fire began none of my employees were on the site. We respected all procedures," Julien Le Bras, a representative of family firm Le Bras Freres.
Officials breathed a sigh of relief that many relics and artworks had been saved. At one point, firefighters, policemen and municipal workers formed a human chain to remove the treasures, including a centuries-old crown of thorns made from reeds and gold, and the tunic believed to have been worn by Saint Louis, a 13th century king of France.
"Notre-Dame was our sister, it is so sad, we are all mourning," said Parisian Olivier Lebib. "I have lived with her for 40 years. Thank God that the stone structure has withstood the fire."
Reporting by Sudip Kar-Gupta, Inti Landauro, Richard Lough, Sarah White, Emmanuel Jarry and Luke Baker in Paris; Additional reporting by Philip Pullella and Michelle Martin in Berlin Writing by Richard Lough; Editing by Leigh Thomas, Raissa Kasolowsky and Peter Graff