Paris’ police department will now investigate any “involuntary destruction caused by fire”, a spokesperson said.
Notre Dame continued to burn behind Mr Macron as he spoke late on Monday.
“The worse has been avoided although the battle is not yet totally won,” he said.
“Notre-Dame is our history, our literature, part of our psyche, the place of all our great events, our epidemics, our wars, our liberations, the epicentre of our lives.”
“Notre-Dame is burning, and I know the sadness, and this tremor felt by so many fellow French people. But tonight, I’d like to speak of hope too,”
The French president said a national fundraising campaign to restore the cathedral would be launched on Tuesday.
He called on the world’s “greatest talents” to help with the effort.
“Let’s be proud, because we built this cathedral more than 800 years ago, we’ve built it and, throughout the centuries, let it grow and improved it. So I solemnly say tonight: we will rebuild it together,” he said.
Mr Macron also praised the “courage” of firefighters who worked through Monday night, trying to save the landmark.
The fire began on Monday evening, with first reports emerging of smoke in the cathedral shortly before 6pm.
Visitors were evacuated and the Paris Fire Brigade began to fight flames which had emerged from the cathedral’s roof.
Notre Dame’s spire has collapsed in flames but firefighters are optimistic that its two iconic towers have been saved.
Additional reporting by agencies