The minister said Mohamed Lahouaiej Bouhlel, 31, had had no record of making militant statements and was not known to the intelligence services.
It seems he became radicalized very quickly," Cazeneuve said, without offering specifics.
"This is a new type of attack," Cazeneuve said. "We are now confronted with individuals that are sensitive to the message of ISIS and are committed to extremely violent actions without necessarily being trained by them."
Earlier Saturday, a statement from ISIS' media group, Amaq Agency, said that an ISIS "soldier" carried out the attack in Nice.
The statement, which was posted by ISIS supporters, said a security source told the agency "the person who carried out the run-over in Nice, France, is one of the Islamic State soldiers and carried out the operation in response to calls to target nationals of the coalition which is fighting the Islamic State."
The wording of the statement -- not claiming the attack as an outright act of ISIS, but noting that the attacker was responding to calls to act against the coalition -- mirrors ISIS' language in statements after the nightclub shooting in Orlando, when it claimed gunman Omar Mateen as a "soldier." Forty-nine people died in the June 12 massacre.
French prosecutor François Molins said Friday the attack in Nice fits with calls that "terrorist organizations regularly give out on their videos and elsewhere."
New developments in the investigation
As the investigation continued, French authorities were questioning five people Saturday. Among them was Bouhlel's ex-wife, who was taken into custody Friday, the anti-terrorism prosecutor's office said. The other four are men.
Bouhlel, a resident of Nice, was born in Tunisia but had a permit to live and work in France.
While Cazeneuve said no evidence had yet been found to tie Bouhlel to jihadism, a source close to the investigation told CNN that a phone number belonging to Bouhlel cropped up in a counterterrorism investigation into an associate of Omar Diaby, a 41-year-old Senegalese jihadi who lived in Nice before traveling to Syria.
Diaby, who calls himself Omar Omsen, commands a French jihadi battalion in Syria affiliated with Jabhat al Nusra, al Qaeda's branch in Syria. The source said investigators made the link after cross-referencing case files after the attack in Nice. Investigators are looking into the nature of the links between Bouhlel and Diaby's associate, but they cannot rule out that the two were possibly just part of the same social circle.
French counterterrorism officials have established that a series of YouTube videos Diaby recorded in Nice in 2012 before he departed for Syria helped motivate a significant number of French extremists to travel to fight in Syria. In May, Diaby revealed in a Skype interview with a French journalist that he had faked his own death in August 2015 to get medical treatment outside Syria.
Hollande warns of continued strikes
French President François Hollande, addressing his country after its third major terrorist attack in 18 months
, described the assault as an "unspeakable act."
"We have an enemy who is going to continue to strike all the people, all the countries who have freedom as a fundamental value," Hollande said.
Bouhlel was shot to death by police after he barreled down the crowded Promenade des Anglais for almost a mile, crushing and hitting people who had gathered to watch the Bastille Day fireworks. More than 200 people were injured, and at least 55 of them were in critical condition Friday.
Bouhlel was identified by fingerprints after his identification card was found in the truck, authorities said.
He was known to police because of allegations of threats, violence and thefts over the past six years, and he was given a suspended six-month prison sentence this year after being convicted of violence with a weapon, authorities said.
Bouhlel's father, who lives in Tunisia, said his son showed signs of mental health issues -- having had multiple nervous breakdowns and volatile behavior, said CNN terrorism analyst Paul Cruickshank.
Despite his criminal record, Bouhlel was not on the radar for any kind of terror threat. The man was "entirely unknown by the intelligence services, whether nationally or locally," Molins said.
"He had never been the subject of any kind of file or indication of radicalization."
'There are dead everywhere'
As the seaside resort town tried to regain a semblance of normalcy Saturday, harrowing new details emerged about Thursday night's tragedy. One young victim, Kimberley Torres, described how someone tried to throw her out of the way of the truck, but she was still hit by it.
"I tried to roll myself into a ball, so the people wouldn't crush me, but I was still hit in the stomach and leg," she said.
The 16-year-old, who lives in Nice and is studying for an international baccalaureate, is recovering from her injuries at the Fondation Lenval.
Her mother, Edvige Torres, said she would take her daughter to a psychologist when her physical wounds had healed. She said her daughter called her in tears because she had been separated from her best friend, whom Kimberley was later reunited with and who was unharmed.
"The most awful thing for her, amidst all this is ... she was telling me: 'Mum, there are dead everywhere, severed heads, severed people, there's blood everywhere, mother, come.'"
Edvige Torres said she immediately left her home near the beachfront to find her daughter, whom she then took straight to a hospital.
"I've tried to keep my head until now, but I can't anymore," she said.
'Bodies flying in the air'
Another student said he saw the attack from the balcony of his friends' flat.
Andres Farfan, a 21-year-old from Peru, was celebrating finishing his university degree in Nice when he heard screams coming from the beachfront.
He looked down and saw the truck speeding on the footpath of the road.
"It was going pretty fast, I guess 60 or 70 kph, and people were screaming and trying to avoid it, and some jumped to the beach side, and it is not small sized, it's a big jump," Faran said.
Most people on the boulevard struggled to avoid the truck as it approached.
"At that point I thought that these people wouldn't make it, because it was really fast and they were all together like a pack," he said. "I couldn't watch it. I closed my eyes, and I went inside the apartment. Some of my friends did the opposite -- they went outside, when people started screaming, they went and saw this; then they started screaming and crying immediately. I can't imagine what they have seen.
"They say they saw bodies flying in the air when the truck hit them."
Farfan braced himself to go out on the balcony to see the aftermath. "We saw the first scenes of the bodies, the uncovered bodies, the dead. I saw a bunch of six, seven bodies -- they were stuck to the floor with blood around them. It was horrible to watch."
Before the attack
Bouhlel began the attack about 10:45 p.m., authorities said. At one point, he fired a gun several times at three police officers close to a hotel, the prosecutor said.
The truck he used was rented on Monday and was supposed to have been returned Wednesday, Molins said, without specifying who rented it. Surveillance video shows that about two hours before the attack Thursday, Bouhlel rode a bicycle to pick up the truck east of the city, the prosecutor said.
After Bouhlel was shot, police found a handgun and some ammunition in the truck's cab, as well as a replica handgun, two replica assault rifles, a cell phone and various documents, Molins said. In the trailer was the bicycle and some empty pallets.
Hollande declared a national mourning period from Saturday to Monday.
France was just preparing to lift its state of emergency, which was put into place in the wake of the November terror attacks in Paris that killed 130 people, the deadliest attack in France's history.
Nice is just the latest city to be hit by a terror attack. Istanbul, Orlando, Baghdad, Brussels and Dhaka in Bangladesh are among other targets hit in recent months.
'Big step back'
Cruickshank said "no country in the Western world is threatened more by jihadis and terrorism than France."
"This is a big step back here. They are absolutely exhausted after a year and a half of intense efforts to try and protect this country," Cruickshank said.
"The painful reality here is that if it wasn't going to be this promenade, it would have been any other promenade."
France had put intense security in place for Euro 2016
, the international soccer tournament that just ended. No major attacks occurred during the event.