The man, a former journalist who was working on a doctoral thesis, can be seen lunging at officers outside the cathedral with a hammer, then being shot to death.
The suspect who was also armed with knives, shouted "This is for Syria" when he attacked the policeman and slightly injured him, according to the minister.
Le Figaro claims the investigation into the man's home uncovered a video where the attacker pledged his loyalty and allegiance to Islamic State.
The Local fr reports that a government spokesperson said that the attack was an "isolated act", and that the alleged attacker, Farid Ikken, had "never showed any sign of radicalization".
At a defense council held in Paris on Wednesday, French President Emmanuel Macron decided on a new body including all the country's intelligences services to better coordinate response to eventual terror risk, his office said.
Castaner said it "is very hard to anticipate" attacks when they were staged by people who were not on the police radar.
The performance of France's intelligence services has come under close scrutiny since the November 2015 attacks in Paris, when militant gunmen and suicide bombers struck entertainment venues across the capital, killing 130 people.
More than 230 people have been killed in a wave of attacks in France either claimed by or inspired by Daesh over the past two-and-a-half years.
The 40-year-old man had pledged allegiance to the Islamic State group, it emerged earlier Wednesday, but his family voiced shock and officials said he was not known to intelligence services.
The new task force will include some 20 people representing the various security services and be operational 24 hours, seven days a week.
A 22-year-old officer received injuries to his neck during the attack, which happened while around 1,000 people were inside the cathedral. "Then there was a crowd surge and people panicked".
The suspect's thesis director at the University of Lorraine, where he enrolled in 2014, said he had shown "no outward sign of an excessive adherence to Islam".
Police block off the streets near Notre Dame Cathedral in Paris, France, June 6, 2017.
"So we are trapped in Notre Dame Cathedral".
"When I knew him, he had a pro-Western, pro-democratic outlook", Arnaud Mercier told BFMTV.