"There is no more risk the edifice's walls could fall down", Lt. Col. Gabriel Plus, chief spokesman for the Paris fire service, told The Associated Press.
Frank Riester, France's culture minister, said the cathedral's vaulted ceiling is still "in an emergency situation".
"We mustn't say "the cathedral is closed for five years and that's it", he said, according to the BBC.
Many protesters were deeply saddened by the fire at a national monument.
In fact, some protesters have said Monday's fire and the quick outpouring of some $850 million to rebuild further highlighted the differences between France's wealthy and the working, middle class.
Newspaper Le Parisien reported that a computer bug could have misdirected firefighters responding to the initial fire alarm.
Some prominent yellow vest figures who had stopped protesting recently said they would return to the streets on Saturday, out of an even greater sense of being overlooked since the Notre Dame tragedy.
Nice weather today, some severe weather likely tomorrow
Pick out the safest room of the building you are in (lowest level, interior, away from windows) and have a way to access alerts. If you must travel, make sure to check the weather conditions, watches , warnings and advisories before venturing out the door.
Rector Chauvet added that there were fire alarms throughout the ancient building, describing it as "well protected".
"We'll rebuild Notre-Dame even more handsome and I want it to be completed in five years, we can do it", said Macron, who has already launched a massive fundraising campaign for the project, garnering around a billion dollars in pledges.
In the past week, almost $1 billion has been raised from to rebuild the iconic cathedral, including a total of 300 million euros from French billionaires Bernard Arnault and François-Henri Pinault. He has named a general, Jean-Louis Georgelin, former chief of staff of the armed forces, to lead the reconstruction effort.
Nearly $1 billion has been donated to the reconstruction.
"I was incredibly sad about Notre-Dame because it's such a lovely building", Mr Géant said in an interview with CNN.
The Notre Dame fire delayed Macron's long-awaited plans to quell anti-government protests that have marred his presidency.
"Notre-Dame is a beacon of hope and beauty that has defined the heart of Paris and the soul of France for centuries", Disney Chairman and CEO Robert Iger was quoted in a statement Wednesday announcing the donation.