He said the driver has been shot dead by police. They are currently hunting for a second attacker, according to reports.
French media reports said that as well as the dead, a further 15 people were critically injured and dozens more wounded.
Nice prosecutor Jean-Michel Prette said bodies were strewn about along the road.
The Gendarmerie Nationale tweeted: 'Emergency operation in progress. Keep calm and avoid downtown area. Follow the official accounts to be informed.'
Bodies could be seen lying on the floor by the beach, as the police and other emergency services tried to deal with a mass panic.
British holidaymaker Esther Serwah, 59, was staying in a hotel a short walk from the scene.
She said she had been on her way to the Promenade des Anglais for dinner with her daughters when people started screaming at her.
Mrs Serwah, from Surrey, said: 'I was just walking to the Promenade and then I saw everybody running and I just didn't know what was going on.
'People were screaming at me in French but I didn't understand.
'Some people were lying on the streets dead and people were running over the bodies.
'Everybody was saying it's a terrorist attack. It's just horrible, horrible, horrible.
'I'm in shock. I'm still shaking.'
European Council president Donald Tusk said Europe stands united with the French people in the battle against violence and hatred, while Belgian foreign minister Didier Reynders both described the attack as 'barbaric'.
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Soldiers secured the scene while emergency workers treated the wounded and checked on those killed in yesterday's massacre
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Local businesses were used as triage centres to treat those who were not badly injured in last night's terrorist massacre
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Within an hour of the attack, French authorities had handed over the investigation to anti-terrorist police
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The Hotel Negresco was used as a make-shift triage centre to house survivors of last night's terrorist attack
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At least 15 people are believed to be in a critical condition following last night's terrorist attack in Nice
US President Barack Obama has condemned what appears to be 'a horrific terrorist attack' and has directed his officials to provide any assistance required by the French government.
He said: 'On behalf of the American people, I condemn in the strongest terms what appears to be a horrific terrorist attack in Nice, France, which killed and wounded dozens of innocent civilians.
'We stand in solidarity and partnership with France, our oldest ally, as they respond to and recover from this attack.
'We know that the character of the French Republic will endure long after this devastating and tragic loss of life.
'On this Bastille Day, we are reminded of the extraordinary resilience and democratic values that have made France an inspiration to the entire world.'
His Secretary of State John Kerry added: 'The horrendous attack in Nice is an attack against innocent people on a day that celebrates Liberty, Equality, and Fraternity.
'On behalf of all Americans, and especially the great many with close ties to France, I offer our deepest condolences to the friends and family of those who were killed and our hopes for a speedy recovery to those who were injured.
'I was proud to stand alongside French leaders earlier today at Bastille Day celebrations in Paris, and the United States will continue to stand firmly with the French people during this time of tragedy. We will provide whatever support is needed.
'Our embassy in Paris is making every effort to account for the welfare of U.S. citizens in Nice. Any U.S. citizens in Nice should contact friends and family directly to inform them of their well being.'
.
French media reports said that as well as the dead, a further 15 people were critically injured and dozens more wounded.
Nice prosecutor Jean-Michel Prette said bodies were strewn about along the road.
The Gendarmerie Nationale tweeted: 'Emergency operation in progress. Keep calm and avoid downtown area. Follow the official accounts to be informed.'
Bodies could be seen lying on the floor by the beach, as the police and other emergency services tried to deal with a mass panic.
British holidaymaker Esther Serwah, 59, was staying in a hotel a short walk from the scene.
She said she had been on her way to the Promenade des Anglais for dinner with her daughters when people started screaming at her.
Mrs Serwah, from Surrey, said: 'I was just walking to the Promenade and then I saw everybody running and I just didn't know what was going on.
'People were screaming at me in French but I didn't understand.
'Some people were lying on the streets dead and people were running over the bodies.
'Everybody was saying it's a terrorist attack. It's just horrible, horrible, horrible.
'I'm in shock. I'm still shaking.'
European Council president Donald Tusk said Europe stands united with the French people in the battle against violence and hatred, while Belgian foreign minister Didier Reynders both described the attack as 'barbaric'.
+45
Soldiers secured the scene while emergency workers treated the wounded and checked on those killed in yesterday's massacre
+45
Local businesses were used as triage centres to treat those who were not badly injured in last night's terrorist massacre
+45
Within an hour of the attack, French authorities had handed over the investigation to anti-terrorist police
+45
The Hotel Negresco was used as a make-shift triage centre to house survivors of last night's terrorist attack
+45
At least 15 people are believed to be in a critical condition following last night's terrorist attack in Nice
US President Barack Obama has condemned what appears to be 'a horrific terrorist attack' and has directed his officials to provide any assistance required by the French government.
He said: 'On behalf of the American people, I condemn in the strongest terms what appears to be a horrific terrorist attack in Nice, France, which killed and wounded dozens of innocent civilians.
'We stand in solidarity and partnership with France, our oldest ally, as they respond to and recover from this attack.
'We know that the character of the French Republic will endure long after this devastating and tragic loss of life.
'On this Bastille Day, we are reminded of the extraordinary resilience and democratic values that have made France an inspiration to the entire world.'
His Secretary of State John Kerry added: 'The horrendous attack in Nice is an attack against innocent people on a day that celebrates Liberty, Equality, and Fraternity.
'On behalf of all Americans, and especially the great many with close ties to France, I offer our deepest condolences to the friends and family of those who were killed and our hopes for a speedy recovery to those who were injured.
'I was proud to stand alongside French leaders earlier today at Bastille Day celebrations in Paris, and the United States will continue to stand firmly with the French people during this time of tragedy. We will provide whatever support is needed.
'Our embassy in Paris is making every effort to account for the welfare of U.S. citizens in Nice. Any U.S. citizens in Nice should contact friends and family directly to inform them of their well being.'
.