Islamic State has claimed responsibility for the Nice terror attacks in a media statement, Fox News and Associated Press have reported.
The claim comes as four men believed to be linked to the Tunisian man who killed 84 people when he drove a truck into a Bastille Day crowd in Nice were arrested overnight, a judicial source said.
One of the men being held was arrested Friday and three others on Saturday morning, the source added. The driver's estranged wife is also still being held by police.
Investigators are trying to establish if the driver was motivated by radical Islam.
There has been no claim of responsibility for the attack in which Mohamed Lahouaiej-Bouhlel, 31, smashed a 19-tonne truck into a mass of people celebrating France's Bastille Day in the Riviera city of Nice.
Some 30,000 people had thronged the Promenade Des Anglais to watch a fireworks display with their friends and families on a night which turned to horror as the rampaging truck left mangled bodies strewn across the palm-fringed road.
President Francois Hollande said the country would observe three days of mourning as he warned the death toll could rise further, with more than 50 people still fighting for their lives.
The massacre, which comes after two major terror attacks in France in 2015, has once again shaken the country to its core, raising questions over intelligence and security failings and how to stop such unsophisticated, yet deadly, assaults.
Hollande was due to meet his security chiefs on Saturday and the country would observe a minute of silence at midday.
Investigators were piecing together a profile of the driver, Lahouaiej-Bouhlel, a man with a record of petty crime, but no known connection to terrorist groups.
Prime Minister Manuel Valls said the attacker probably had links to radical Islam, but Interior Minister Bernard Cazeneuve cautioned it was too early to make the connection.
- A depressed loner -
Anti-terrorism prosecutor Francois Molins said the 31-year-old Tunisian was "completely unknown" to the intelligence services but that the assault was "exactly in line with" calls from jihadist groups to kill.
For several years, extremist groups such as Islamic State and Al-Qaeda have exhorted followers to strike "infidels" -- singling out France on several occasions -- using whatever means they have at hand.
In September 2014, IS spokesman Abu Mohammed al-Adnani, suggested supporters "run (infidels) over with your car".
While some attacks on the west -- such as the November assault on Paris and the March bombings in Brussels -- are carried out by jihadists who have been to the centre of IS operations in Iraq and Syria, others have been led by so-called "lone-wolf" attackers.
Inspired from afar by Islamist propaganda, such attackers are a massive headache for intelligence services.
Lahouaiej-Bouhlel's father said he had suffered from depression and had "no links" to religion.
"From 2002 to 2004, he had problems that caused a nervous breakdown. He would become angry and he shouted... he would break anything he saw in front of him," Mohamed Mondher Lahouaiej-Bouhlel said in Tunisia.
"We are also shocked," he said.
- Eiffel Tower catches fire during Bastille Day fireworks
- Footage shows truck loaded with guns unleashing attack on Nice crowd on Bastille Day* Eiffel Tower catches fire during Bastille Day fireworks
- Footage shows truck loaded with guns unleashing attack on Nice crowd on Bastille Day
Neighbours described the attacker, who lived in a modest district of Nice and worked as a delivery man, as a loner who never responded to their greetings.
He and his wife had three children, but she had demanded a divorce after a "violent argument", one neighbour said.
His wife was arrested on Friday and taken for questioning, a police source said.
- 'Bodies flying in the air' -
In Nice, the seaside streets that would normally be bustling on a summer weekend were near-deserted, with teary residents making their way to the promenade to lay down flowers in memory of the dead.
Photographs after the carnage showed the truck, which had been hired on Monday, with its front badly damaged and riddled with bullet holes.
Molins said a fake pistol, fake rifles and a dummy grenade were found inside.
One woman, Nataje, 52, said she heard a "boom" as the truck began accelerating into spectators on the Promenade des Anglais, the showpiece coastal road in the southern French city.
"I turned round and I saw the truck which was crashing into the crowd and bodies flying into the air," the Nice resident said.
"It was horrible. I saw a father with his two-year-old son in his arms. The child was dead."
At least 10 children and teenagers were among the dead.
Some 200 people were injured in the assault, among them around 50 children, with some "hanging between life and death", a hospital official said.
"There are French among the victims and also many foreigners from every continent and many children, young children," Hollande said after visiting a hospital.
Two US citizens, a Russian woman, a Ukrainian, two Swiss nationals and three Germans were among those killed.
Hollande described the incident as a "terrorist attack" in a sombre televised address, adding that "France was struck on its national day... the symbol of freedom".