A further 18 people are in a critical condition and French president Francois Hollande said the country's state of emergency would be extended for a another three months.
A lorry hit crowds who had gathered to celebrate the French national day in the Mediterranean city on Thursday night.
Mr Hollande led a wave of tributes from world leaders saying: "France has been hit by a tragedy once again. This monstrosity of using a lorry to deliberately kill people, many people, who only came out to celebrate their national day.
"France is in tears. It is hurting but it is strong, and she will be strong, always stronger than the fanatics who wish to hurt us."
He also said that a military operation was in place that would allow the mobilisation of 10,000 military officers and that police from across the country would be called to assist their colleagues in Nice.
The country borders will be tightened and would show "real force and military action in Syria and Iraq", Mr Hollande said.
Regional hospitals have been warned to expect an influx of the injured and the president urged citizens to be aware of security over the busy national holiday weekend.
In a press conference at the scene, French interior minister Bernard Cazeneuve said that the identification of the criminal was in progress, refusing to confirm reports that an ID card was found after police shot dead the lorry driver, and added that more information on the issue would come from the prosecutor's office.
"We are in a war with terrorists who want to strike us at any price and in a very violent way," the minister said.
French prosecutors earlier said they had launched a terrorism investigation after the lorry careered through the packed seafront for hundreds of yards as crowds watched fireworks.
Nice regional president Christian Estrosi said guns and grenades were found in the lorry, whose driver was shot dead by police.
The politician, who was at the celebration when the carnage happened, said: "This is the worst Nice drama of history.
"We are terrified and we want to present to all the families our sincere condolences.
Nice prosecutor Jean-Michel Prette said bodies were strewn about along the road.
Mr Brandet said no hostages had been taken and the lorry driver had been "neutralised", adding that authorities were investigating if he acted alone.
Pictures and footage shown on social media showed crowds fleeing in terror from the scene on the Promenade des Anglais, which was busy with revellers celebrating and watching fireworks.
Eyewitnesses reported hearing gunshots and pictures on social media showed armed police with weapons trained on a badly damaged white lorry with bullet holes in the windscreen.
France is still on alert after the Paris terror attacks on November 13, in which 130 people were killed at sites including the Bataclan Theatre and Stade de France.
The state of emergency initiated after those attacks which has now been extended was due to be lifted later this month.
Lawyer Harjit Sarang was among those caught up in the terror with her children.
The Londoner tweeted: "Running through crowds in Nice with kids and terrified. Never taking kids to a public event again. Finally back to hotel. Hate this!"
A Foreign Office spokeswoman said: "We are deeply concerned about reports of an incident in Nice and are in touch with the local authorities to seek more information.
"Our thoughts are with those affected and we stand by to help any British nationals."
A Downing Street spokesman said: "The Prime Minister is being kept updated on reports coming in from Nice.
"We are shocked and concerned by the scenes there. Our thoughts are with all those affected by this terrible incident on what was a day of national celebration.
"The FCO are in touch with the local authorities to seek more information and we stand ready to help any British nationals and to support our French partners."
New Foreign Secretary Boris Johnson tweeted that he was "shocked and saddened by the appalling events in Nice, and the terrible loss of life".
A Rihanna concert scheduled for Friday night at the Allianz Riviera stadium in Nice has been cancelled, as have the city's jazz festival which was due to run from Saturday to Wednesday and some of the Bastille celebrations over the weekend.
Briton Will Shore told BBC Radio 4: "It was quite chaotic really. There was a lot of people screaming, running around and people were kind of being pushed over, I think, from people just being so frightened about what was going on especially after hearing the gunshots.
"I had to help a couple of people up who were in distress on the floor because everyone was in such a panic."
Kevin Harris watched the attack unfold from his balcony.
He told the BBC: "I saw what appeared to be be bodies in the lying in the road.
"I spoke to my neighbour who said the lorry had ploughed through the people.
"It's a terrible scene."