He said Bouhlel had received a six-month prison sentence in March for a conviction for assault with a weapon, but other legal officials said his sentence was suspended because it was his first conviction.
Chief prosecutor Francois Molins said police risked their own lives trying to stop the truck as it travelled two kilometres down the promenade.
The attacker, 31-year-old Mohamed Lahouaiej Bouhlel, was slowed when a heroic member of the public leapt onto the vehicle and wrestled the driver. As the truck careened down Nice's famous Promenade des Anglais, which runs along the Mediterranean Sea, it hit Mehdi and Tata, killing them instantly.
The truck used in a deadly attack in Nice, France can be seen in the distance.
Cazeneuve told broadcaster TF1 that the attacker was not known to intelligence services and said he could not confirm his motives were linked to jihadism.
Meanwhile, Belgium's Deputy Prime Minister and Minister of Foreign Affairs Didier Reynders said that among the victims of the terrorist attack there might be a Belgian citizen of the Russian origin and a woman of Kazakhstan's origin, both residing in Antwerp.
Molins said Bouhlel's ex-wife is in custody as police try and determine whether he "had ties to Islamist terrorist organisations".
The children's hospital in Nice says it has treated dozens of children and teenagers injured in the attack, the AP adds. "But in that moment as I was considering it, that's when the panic really took hold".
School District 68 officials confirmed that a group of students and chaperones in Nice were safe in a tweet at around 5 p.m. on Thursday. "They didn't know where to go, they were looking for an exit - they were hoping they'd find an exit out the back".
French president Francois Hollande, speaking prior to a vigil at Nice cathedral last night, said: "France is in tears".
"We pledge to stand with our French friends as we defend our nations against this scourge of terrorism and violence", he said.
Valls said French President François Hollande had called for three days of mourning, from Saturday to Monday.
"France was struck on the day of its national holiday, July 14, the symbol of liberty", said Hollande.
While no group has come forward to take responsibility for the attack, Islamic State militants have been praising Bouhlel's tactics, reports Vocativ. "And that is exactly where that truck still is right now", Rapp said.