A man was arrested on Friday and three other men were taken in by police early Saturday, according to French news agency AFP.
Authorities are trying to determine whether Bouhlel, who had lived in Nice for years, was acting alone in the deadly attack.
The Islamic State group has claimed responsibility for the attack, though people close to him noted no signs of radicalism, just anger.
With scores still hospitalized, France's health minister is visiting Nice.
Officials said that 202 people had been wounded in the attack, with 25 of them on life support late Friday.
France on Saturday began three days of national mourning in homage to the victims - although that hasn't stopped politicians from sniping at each other over who bore responsibility for the failing to stop the attack.
In an open letter published on the Nice Matin newspaper's website, regional council President Christian Estrosi - a member of France's opposition Republicans - described the country's current Socialist leadership as "incapable." He said he had requested that the police presence be reinforced in Nice ahead of the fireworks display but was told there was no need.
Cazeneuve, speaking at the Elysee, disagreed, saying that high security had been assured in the region - including at the Cannes Film Festival and the Nice Carnival. Government spokesman Stephane Le Foll warned against attempts to divide the country, calling for "unity and cohesion."
France is heading into elections next year, and the deeply unpopular President Francois Hollande is facing multiple challengers, from within his own Socialist Party, from the right-wing Republicans and from the far-right National Front.
- with AP
