The driver, identified by a police source as a 31-year-old Tunisian-born Frenchman, also appeared to open fire before officers shot him dead, Reuters reports.
The man was not on the watch list of French intelligence services, but was known to the police in connection with common crimes such as theft and violence, the source said.
Interior Minister Bernard Cazeneuve said 18 people were in a critical condition after the attack on Thursday night, when the white truck zigzagged along the seafront Promenade des Anglais as a fireworks display marking the French national day ended just after 10:30 p.m. (4:30 p.m. ET).
According to one city official, the truck careered on for up to two km (1.5 miles). Several children were among the dead.
The attack seemed so far to be the work of a lone assailant.
Hollande said in a pre-dawn address that he was calling up military and police reservists to relieve forces worn out by enforcing a state of emergency begun in November after Islamic State gunmen and suicide bombers struck Paris entertainment spots on a Friday evening, killing 130 people.
Only hours earlier he had announced the emergency would be lifted by the end of July. Following the attack, he said it would be extended by a further three months.
“France is filled with sadness by this new tragedy,” Hollande said. “There’s no denying the terrorist nature of this attack.”
Major events in France have been guarded by troops and armed police since the Nov. 13 attacks. But it appeared to have taken many minutes to halt the progress of the truck as it tore along pavements and a pedestrian zone.
One witness said she thought the attacker was firing a gun as he drove.
“I saw this enormous white truck go past at top speed,” said Suzy Wargniez, a local woman aged 65 who was watching from a cafe on the promenade. “It was shooting, shooting.”
A local government official said weapons and grenades were later found inside the rented vehicle.
Image: Reuters\Philippe Wojazer.