Five people have been arrested following the Bastille Day attack, which injured more than 200 people on the Promenade des Anglais, according to officials.
Inquiries were continuing into whether 31-year-old driver Mohamed Lahouaiej Bouhlel acted alone or had accomplices before he drove a 19-tonne hired truck at speed into scores of people before he was shot dead by police.
The driver was a “soldier” of Islamic State, the group’s media outlet said.
The Aamaq news agency quoted a source as saying the attacker had responded to calls “to target the citizens of coalition countries fighting the Islamic State”.
The language used implied that he may have acted independently and there was no evidence IS was involved in planning the atrocity.
The IS claim of responsibility came after the French authorities said Bouhlel had no known links with terrorists, unlike those behind previous attacks in Paris.
Officers carried out a raid at an address near Nice’s main train station on Saturday morning and made two arrests, Europe 1 reported. They were thought to be known to the killer.
A third person was also arrested at an address in Nice earlier in the morning.
According to reports, the terrorist’s ex-wife was being questioned on Friday.
The woman who was estranged from him and had been subject to his domestic violence, was taken into custody for her own protection, French media reported.
The driver’s father has said that Bouhlel had received psychiatric treatment in the past.
The Queen added her voice to the wave of sympathy from leaders across the world as the country faced another terrorist attack, following those in Paris in November, in which 130 died, and in January 2015 in which 17 were killed.
President Francois Hollande said 50 people were “between life and death”, while several people were among the missing and a “small number” of Britons were injured.
On Friday night the Foreign Office advised Britons in Nice to follow the instructions of the French authorities, who have cancelled public events over the weekend.
A vigil took place at Nice Cathedral on Friday night and mourners also gathered at a makeshift memorial amid a visible police presence near the promenade, which is closed to the public.
Revellers in the resort initially thought the commotion was part of a celebratory firework display, but then saw the lorry and assumed the driver had lost control.
Jan Jeffreys and her partner Les Smith, from Shropshire, were enjoying their first evening in Nice when the attack happened.
They described a chaotic scene as people tried to run out of harm’s way.
Ms Jeffreys, 53, said: “There were people in cars turning round on grass verges, reversing. It was just mayhem.”
Mr Smith said he was haunted by images of bodies lying in the street.
The 63-year-old businessman said: “The first body that I saw was covered in a sheet and was quite obviously a heavily pregnant woman. It was very upsetting. I keep seeing it. I just can’t understand why this happened.”
Another couple from Dungannon, Co Tyrone, said they saw a mood of celebration turn to one of fear as they watched the tragedy unfold from their holiday apartment balcony.
Philip Rodgers, 67, in the city with his wife Yvonne, described “tremendous fireworks, crowds and crowds of lovely families, then panic. Very, very frightening”.
He said it went from “pure happiness to fear”.
Prime Minister Theresa May has said Britain must redouble its efforts to defeat “brutal” terrorist “murderers”, while police forces across England and Wales have been told to review security at major events over the next week in the wake of the bloodbath.
Foreign Secretary Boris Johnson, who had celebrated Bastille Day with dinner at the French embassy in London, described the attack as “appalling and cowardly”.
The Association of British Travel Agents (Abta) issued a statement encouraging people to check with their tour operators before heading to France.
There was a visible security presence in the city on Saturday morning.
Soldiers patrolled the front of the main train station.
Stallholder Romain Ribero said the French are used to high security in the wake of the Paris massacre last year.
He said: “We are a bit wary of bomb attacks so we are used to the security.”