He injured four people before he was shot and killed.
French officials couldn't confirm that Bouhlel had been approached by an Algerian recruiter.
Imam says many Muslims among Nice attack victims.
Saturday's arrests concerned his "close entourage", police sources said.
Police identified the attacker as Mohamed Bouhlel, a 31-year-old Nice resident.
President Enrique Peña Nieto condemned the attack in the Southern France city that left at least 60 people dead.
Police shot and killed the driver, who drove at high speed for over 100 meters (yards) along the famed Promenade des Anglais seafront before hitting the mass of spectators.
Local media said at least 30 were dead after the truck drove through people on the famed Promenade des Anglais on the Nice seafront.
Five others were wounded outside the mosque where Muhammad is buried in Medina.
Alan Ramírez is in stable condition.