But the statement quoting a security member of the group said the man was following calls from IS to target nationals of countries fighting it.
France's president said some 50 people are critically injured, many of them children.
Interior Minister Bernard Cazeneuve said France has no evidence that Bouhlel had ties to IS.
The attack Thursday night on France's national holiday rocked a nation still dealing with the aftermath of attacks in November in Paris that killed 130 and in January 2015 that killed 17.
Defense and intelligence leaders were gathering at the Elysee Palace, the official residence of the French president, for talks about the atrocity, the third mass casualty attack against France in 18 months, the news agency said.
"I wanted to see the paradise", he said.
The Library of Birmingham was being lit up in red, white and blue tonight as France mourned the Nice terror attack which claimed more than 80 lives.
The president said that the fight against ISIS and other terrorist groups will require the U.S.to not give up on diplomacy to end the Syrian civil war, for example, and to work with Muslims around the world.
"They are also using the public perception that an attack like this seems to fit Islamic State".
President Barack Obama on Friday decried the deadly truck attack in Nice as a "tragic and appalling" on freedom and pledged firm USA support for France.
"On behalf of the people of Birmingham, I extend deepest sympathies for the many victims killed and injured and offer condolences to their families and friends".
At least three people were detained early on Saturday in the French city, Reuters reported police sources had said.
"Yesterday in all mosques in the region of Alpes-Maritimes, there has been a common prayer calling for vigilance and patience, because these very bad events affect us; and there has been a call for blood donation", he said.
Bouhlel, 31, was shot dead by officers at the scene.
Video from Nice showed armed police chasing the truck on foot as it raced along a seaside street, running down people who had been heading home after a Bastille Day fireworks display. But neighbors in the Nice neighborhood where the Bouhlel used to live told The Associated Press his estranged wife had been taken away by police on Friday.