The man suspected of carrying out the terror attack in Nice is said to be a 21-year-old Tunisian.
The African country started an investigation on Thursday evening after that report came out.
The man is said to have arrived in Europe as a migrant on the Italian island of Lampedusa in September.
After a period of quarantine, he was released with a message to leave Italy, before arriving in France in October.
At least three people were killed in the attack in Notre-Dame of Nice.
They were stabbed on Thursday morning around 9 a.m., after which the perpetrator was shot.
French media reported that six were also injured and one victim was beheaded, but that has not been confirmed by the authorities.
All of France has been scaled up to the highest threat level because of the terrorist attack, Prime Minister Jean Castex told a press conference on Thursday.
This allows the government to take more security measures throughout France.
Later this evening, at 9 p.m., the French counter-terrorism prosecutor will hold another press moment.
It is not clear whether some measures will be announced by then.
Incidents in several French cities
An incident took place not only in Nice.
Two hours after the attack, a man was shot dead in the French city of Avignon who threatened passers-by with a knife.
It would be a confused man who is in treatment with a psychiatrist and has disjointed thoughts.
In addition, an Afghan man was arrested in Lyon wearing a djellaba and combat clothing, armed with a 30-centimeter knife.
Finally, a guard from the French consulate in the Saudi city of Jeddah was stabbed.
He has been hospitalized.
European leaders say they are "shocked" by the attacks in and against France.
In a joint statement they speak of "terrorist attacks" and show solidarity with France.
"We call on leaders around the world to work toward dialogue and understanding between communities and religions, rather than division."
Prime Minister Mark Rutte also responded briefly to the attack in France.
"For the second time in a short time, France is startled by a gruesome act of terrorism, this time in Nice. Our thoughts go out to the relatives. And we say to the French people: you are not alone in the fight against extremism. The Netherlands is next to you. . "
See also: Multiple incidents in France: why is the country so restless?