The IS issued a statement to press agency Amaq, BFMTV reported. Mohamed Lahouaiej Bouhlel, who ran over the victims in Nice with a truck, was described as a "soldier" of the IS.
The attack was in response to the group's call to target the anti-IS alliance, Xinhua news agency cited a source as saying.
A terrorist sped a rented truck through a crowd of thousands enjoying Bastille Day celebrations in Nice on Thursday night.
The attack also left over 200 people injured, a third of whom were battling for life.
French President Francois Hollande flew to Nice, met the wounded and said the terrorist struck the crowd "merely to satisfy the cruelty of an individual -- and maybe a group".
Hollande extended the state of Emergency in France for three more months beyond July 26 and called in the reservists. A three-day national mourning began from Saturday.
Besides driving over people, the driver, who was known to police but not to intelligence agencies in France, fired at the crowd, creating more mayhem.
It was the worst terror attack in France since terrorists struck in Paris in November 2015, killing 130 people and injuring over 250.
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