The Paris prosecutors' office says investigators are treating the blaze that destroyed part of Notre Dame as an accident for now.
French President Emmanuel Macron arrives at the front entrance of the cathedral.
Both the spire and roof of the cathedral collapsed and footage from the scene showed flames inside one of the building's two towers.
A catastrophic fire engulfed the upper reaches of Paris' soaring Notre Dame Cathedral as it was undergoing renovations Monday, threatening one of the greatest architectural treasures of the Western world as tourists and Parisians looked on aghast from the streets below.
The Vatican has expressed its shock and sadness, and in chiming in on Twitter with his version of sympathy, President Trump suggested using flying water tankers to fight the blaze - a suggestion French officials quickly brushed off saying it could collapse the entire structure of the landmark church.
Have you taken a favourite photo of Notre Dame?
Top image: The Notre Dame Cathedral in Paris on fire.
A firefighter at the scene said all efforts were being directed at saving the northern tower and the artwork at the back of the cathedral.
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Police in the capital said there were no deaths so far and the origin of the fire was unknown.
The cathedral was in the midst of renovations, with some sections under scaffolding, and bronze statues were removed last week for works.
The cathedral is a world-wide Parisian icon and site of some of the most important moments in the history of France.
"I have a lot of friends who live overseas and every time they come I tell them to go to Notre-Dame", said witness Samantha Silva, with tears in her eyes.
A center of Roman Catholic faith, over the centuries Notre-Dame has also been a target of political upheaval.
"From our hotel room we watched the big tall spire go straight down into the nave of the church", Debbie Furr said.
Mayor Anne Hidalgo said in a Twitter message that firefighters are still trying to limit the fire and urged Paris citizens to respect the security perimeter set up around the cathedral.
"I am following minute by minute the fire that is preying on Notre Dame".