In a statement via its Amaq news service, IS said one of its "soldiers" carried out the attack "in response to calls to target nations of coalition states that are fighting (IS)".
Tunisian Mohamed Lahouaiej-Bouhlel, 31, on Thursday night ploughed a 19-tonne truck into a crowd of people who had been watching Bastille Day fireworks in the French Riviera city, killing 84 and injuring around 300.
After crisis talks in Paris, French Defence Minister Jean-Yves Le Drian noted that IS had recently repeated calls for supporters to "directly attack the French, Americans, wherever they are and by whatever means".
In the wake of its third major terror attack in 18 months, the French government faced searing criticism from opposition politicians and newspapers demanding more than "the same old solemn declarations".
Marine Le Pen, the far-right leader of the National Front party, called on Interior Minister Bernard Cazeneuve to step down.
"In any other country in the world, a minister with a toll as horrendous as Bernard Cazeneuve -- 250 dead in 18 months -- would have quit," she said.
Speaking as France began three days of mourning today, he said Lahouaiej-Bouhlel "had not been known to the intelligence services because he did not stand out... By being linked with radical Islamic ideology".
The interior minister pledged to boost the presence of security forces across the country and called on willing "French patriots" to join the country's operational reservists -- currently made up of 12,000 volunteers.
Police said today they had arrested four more people linked to Lahouaiej-Bouhlel, in addition to his estranged wife who was taken into custody yesterday.
"We are now confronted with individuals open to IS's message to engage in extremely violent actions without necessarily having been trained or having the weapons to carry out a mass (casualty) attack."
At least 10 children and adolescents were among the dead as well as tourists from the United States, Russia, Ukraine, Switzerland and Germany.
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