Islamic State has claimed responsibility for the truck attack in Nice that killed 84 people, injured more than 200 and brought carnage to a Bastille Day fireworks celebration on Thursday night.

In a statement on Saturday, the news agency Amaq, which supports Isis, said: “The person who carried out the operation in Nice, France, to run down people was one of the soldiers of Islamic State. He carried out the operation in response to calls to target nationals of states that are part of the coalition fighting Islamic State.”

Mohamed Lahouaiej-Bouhlel, a 31-year-old French-Tunisian man who lived in the Riviera city, drove a heavy-goods vehicle through a crowd that had gathered to watch the display on Nice’s Promenade des Anglais.

]Later on Saturday, the Isis-operated radio station Bayan claimed that Lahouaiej-Bouhlel was a soldier who had completed a “new, special operation using a truck”. It also warned western nations that no security measures would spare them “from the blows of the mujahideen”.

The claim of responsibility, which came 36 hours after the attack, will increase pressure on French authorities investigating the massacre. No evidence was presented to support the claim that Lahouaiej-Bouhlel had been acting in Isis’s name.

Although President François Hollande has spoken of France facing “the threat of Islamist terrorism”, François Molins, the Paris prosecutor leading the investigation, said Lahouaiej-Bouhlel had no obvious links to radical Islam. He was “totally unknown to intelligence services… and was never flagged for signs of radicalisation”, Molins said.

Neighbours have said the attacker showed no obvious interest in religion.

Five people had been arrested since the attack, according to judicial sources. Agence France-Presse reported that one of the people being held was arrested on Friday, while three others were detained on Saturday morning. The driver’s estranged wife was also being held.

The promenade was reopened on Saturday morning as France began three days of national mourning and Hollande held a security meeting with ministers, police and intelligence officers. As some walked along the thoroughfare beside the beach, others continued to leave floral tributes at the metal barriers lining it.

Lahouaiej-Bouhlel, a Nice chauffeur known to police for petty crimes, accelerated the 19-tonne truck through dense crowds for more than a mile (2km) along the esplanade before police shot him dead.

The death toll is expected to rise. Of the 202 people who were injured, 80 of them were critical, and about 50 were children, many of them seriously wounded. No European attack in recent years has taken such a heavy toll on pre-teens.

] Le Figaro said 16 bodies were still unidentified and five children still critical, three of them on life support, quoting a hospital spokeswoman for the Fondation Lenval, Nice Children’s hospital, which treated 30 children, the youngest aged six months.

A planned memorial ceremony in Nice for the victims on Saturday morning was cancelled for security reasons as the identities of those who died in the attack began to emerge. They included a father and son from Texas, a Moroccon mother of seven who was living in France, a Russian student and French police officer.

Molins said the perpetrator was known to police and had been involved in a series of minor fracas over the last six years, including a violent altercation with another motorist earlier this year for which he received a suspended sentence.

Before the Isis claim was reported, the prosecutor had noted “this sort of thing fits in perfectly with calls for murder from such terrorist organisations”. He said there were two Kalashnikov rifles, bullets and a grenade in the cab of truck, where the driver was killed.

People who lived near Lahouaiej-Bouhlel said they did not think he had attended a mosque.

The attack began shortly before 11pm on Thursday when the truck gained access to the Promenade des Anglais and began mowing down people. Officials said the driver weaved along the road, knocking people down “like skittles”.

Witnesses said people pushed each other out of the way, jumped down to the beach and even ran into the sea to avoid the vehicle. Others described victims being hurled around like mannequins, bodies littering the esplanade in the wake of the zigzagging truck.

A local official said the vehicle was only brought to a stop by the heroics of a person who tried to jump on to the cab. The driver then opened fire before police killed him with a volley of shots through the windscreen.

Most of the dead were French, but there were at least three Germans, two Americans, one Russian, Tunisians and Algerians. A number of Britons were also caught up in the attack.

As investigators continued to comb the vehicle, questions were being asked about how the truck managed to get to the waterfront. The city centre has restrictions on heavy-goods vehicles, and there were additional security restrictions for the festival, including metal barriers.

Hollande is under intense pressure to do more to tighten security. Marine Le Pen, the Front National leader and a rival for next year’s presidential election, called for a “war on Islamic fundamentalism”, saying that all that had happened so far was a “war on words”.

She told Le Figaro: “Nothing that we have proposed has been put in place. Considering the new nature of terrorism, which is now a terrorism of opportunity, that’s to say without hierarchical structure, the urgency is to attack the ideology on which this terrorism is based.”

Alain Juppé, a centre-right presidential hopeful, said: “We know there are faults and shortcomings – the parliamentary inquiry after the November attacks showed us that. We must absolutely lead this struggle against radicalisation and better coordinate our intelligence services.”

World leaders were more sympathetic in their responses. Barack Obama, Angela Merkel and Theresa May all spoke with Hollande to convey their condolences. The Russian president, Vladimir Putin, sent a message to Hollande, saying: “We have sympathy for and solidarity with the French people.”

The father of the truck driver, Monthir Bouhlel, told RTL television in Tunisia that his son had undergone psychiatric treatment in the past, was unstable and sometimes violent. “He had some difficult times. I took him to a psychiatrist, he took his treatments and he said he had a serious illness,” he said. He added that since his son moved to France he had not seen him for four years, and that their last contact was a phone call last week to mark Eid and everything was “normal”.

Corentin Delobel, the lawyer who represented Lahouaiej-Bouhlel when he was given a suspended sentence in March, told RTL: “I could not say ‘he is a terrorist, he’s an Islamist. He’s a radical’. It could have been you or me.”