Prime Minister Manuel Valls said at the weekend that the 31-year-old attacker had been "radicalised very quickly".
Islamic State claimed the attack and hailed Tunisian-born Mohamed Lahouaiej Bouhlel, who drove a truck through a crowd of revellers on the French city's sea-front promenade last Thursday, as one if its soldiers.
Prime Minister Manuel Valls said at the weekend that the 31-year-old attacker had been "radicalised very quickly". The Paris prosecutor said on Monday that, while there was no evidence that he had direct links to Islamic State, he had recently developed an interest in radical Islam.
In Ariane, a district with a big Muslim population a few kilometres from the Abbatoirs neighbourhood where Bouhlel lived, the imam of the local Al Fourkane mosque said radical groups preyed on the weak, and cautioned against focusing on the killer's faith.
"Because the weak are being exploited doesn't mean that we should come down hard on their religion. Quite the opposite. We should be uniting together and defending the country," said Boubekeur Bekri, adding that "a crime is a crime" regardless of faith.
Bouhlel left Tunisia in 2005. His family have painted a picture of a man who suffered "psychiatric troubles" and was prone to depression and violent outbursts. He had several run-ins with the law, including a conviction in March this year for hurling a wooden pallet in a road rage incident.
Relatives and friends of Bouhlel also described a man who at least until recently drank heavily, smoked marijuana and womanised - behaviour at odds with a devout Muslim life.
Elabed Lofti, the imam for Antibes and Juan-Les-Pins, is among Muslim leaders in southeastern France who have distanced their community from the attacker.
"The guy didn't observe Ramadan, the minimum to be considered a good Muslim," he said, referring to the Muslim fasting month that ended late June.
France is home to Europe's largest Muslim minority. In a sign of the growing feeling of alienation among many Muslims in Ariane and elsewhere, Younis, a roof-builder born to Moroccan immigrants, said the whole community was blamed "every time something happens in France, in Europe".
"Once the problem was racial discrimination, now it's religious discrimination," said Younis, who declined to give his surname, sitting at the entrance to a dreary eight-storey block of flats opposite the suburb's small mosque.
For decades Nice, better known for the super-yachts that anchor in its cobalt blue waters and palm-fringed boulevards, has been a gateway for waves of immigrants arriving from France's former colonies such as Tunisia, Morocco and Algeria.
It has also produced the largest contingent of French militants waging jihad in Syria, with about one in 10 originating from the Mediterranean city.
Islamic State has lost much territory in Iraq and Syria this year and some officials fear it may be calling on adherents to conduct high-visibility attacks.