The claim - circulated on social media by a news outlet affiliated with the group - didn't name Mohamed Lahouaiej Bouhlel, the 31-year-old Tunisian who authorities say was behind the wheel as a truck crashed into revelers Thursday night.
Crowds gathered outside the French embassy to remember those killed.
Mr Molins said: "If there are no elements in the investigation to suggest at this stage an allegiance to Islamic State nor links with individuals from the group... he showed a certain recent interest for radical jihadist movements".
IS said the attacker was acting in response to its calls to target civilians in countries that are part of the coalition ranged against it.
"He didn't pray, he didn't fast, he drank alcohol and even used drugs", he said.
Speaking to Le Journal de Dimanche on Sunday, Valls said there was no doubting over Lahouaiej Bouhlel's terrorist motives.
Earlier this month, President Francois Hollande said he did not intend to extend the state of emergency beyond 26 July.
Mourners rallied around Kylan's father, Tahar, who spoke of his grief at losing his son and wife in the attack.
Apparently taken days before he drove into crowds celebrating Bastille Day in the southern French city, the image also shows an unidentified man sitting on the other side of the cab.
France held a national moment of silence Monday for the attack's victims. Touraine, the health minister, urged any survivors to seek counselling offered by the government.
He staked out the site of the carnage in Nice, the Promenade des Anglais, on several occasions before he struck. Some spots are still identifiable by bloodstains.
Joggers, bikers and sunbathers on Sunday cruised down the pedestrian walkway along the glistening Mediterranean Sea, where well-wishers placed flowers, French flags, stuffed animals and candles.
Mr Molins also confirmed 13 victims of the attack are still yet to be identified.
He was shot dead by police when his vehicle's path along the Promenade des Anglais was eventually halted. Neighbors of the man said he hadn't been religious. An argument ensued, with other passers-by saying that his family deserved respect.
He said given his nephew's personal problems in the time leading up to the attack, whoever nudged him to mass murder "found in Mohamed an easy prey for recruitment". The official would not comment on the content of the text messages or confirm reports that they included a request for more weapons.
The state of emergency was put in place following the attacks in Paris last November which left 130 people dead and it gives the police extra powers to carry out searches and place people under house arrest.
Valls defended the government's actions but warned that more lives will be lost to this kind of violence.