IS also claimed responsibility for the November 13 attacks which killed 130 people in Paris, while gunmen in January 2015 attacks on the Charlie Hebdo weekly and a Jewish supermarket were linked to both IS and Al-Qaeda.
The so-called Islamic State group has claimed responsibility for Thursday night's attack in Nice, as three days of national mourning begin in France.
Mr Molins told reporters on Friday afternoon that Bouhlel had shot three police officers before he was killed and his body fell onto the passenger seat.
Investigators are trying to establish if the driver was motivated by radical Islam.
French Police said they had made five arrests in early morning raids in Nice on Saturday in connection with the Bastille Day attack that killed at least 84 people when a truck rammed into crowds in the Riviera city.
About 25 minutes before the July 14 fireworks show, a popular event that draws hundreds of thousands of people to the seafront each year, Lahouaiej-Bouhlel climbed into the vehicle and drove toward the city center.
Vietnam offers profound condolences to the French government, people and families of the victims, and strongly believes that the French government and people will soon overcome the hard moment, he said.
Hollande was due to meet his security chiefs on Saturday and the country would observe a minute of silence at midday.
Lahouaiej-Bouhlel was known to police for petty crimes such as threatening behaviour and theft, but the 31-year-old did not have any links to radicalism and was not on the radar of intelligence services.
I have directed my team to be in touch with French officials, and we have offered any assistance that they may need to investigate this attack and bring those responsible to justice.
The news agency cited an "insider source" saying that "the person who carried out the operation in Nice, France, to run down people was one of the soldiers of Islamic State".
His father said Bouhlel had violent episodes during which "he broke everything he found around him".
"He had a nervous problem - and when he got nervous, he broke everything". "He would become angry and he shouted... he would break anything he saw in front of him", Mohamed Mondher Lahouaiej-Bouhlel said outside his home in the city of Msaken in eastern Tunisia.
"This lorry just mounted the kerb, across the street from us and the next thing, all you could hear was banging and shouting and screaming", he said. But neighbors in the Nice neighborhood where the Bouhlel used to live told The Associated Press that his estranged wife had been taken away Friday by police. The photo shows what appears to be bullet holes in the windshield of the white truck.