A judicial official said the four were in custody on suspicion of association with a terrorist group. Several places were being searched in the probe.
The official, who spoke on condition of anonymity under internal rules, wouldn't give more details.
Interior Minister Gerard Collomb said on France-Inter radio today that the assailant in Sunday's attack had Italian residency and a valid Tunisian passport. The attacker was killed by soldiers after the stabbings, which were claimed by the Islamic State group.
Rome prosecutors opened a terrorism investigation into the suspect, identified in the Italian media as Ahmed Hanachi.
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He had lived in Aprilia, south of Rome, from about 2006 to 2014, Italian news agency ANSA said.
He had a record for petty crimes but no terrorism-related offenses or indications he had been radicalized, Italian daily La Repubblica said.
The reports said he lived in an area with a sizeable Tunisian community, and had married then divorced an Italian woman.
The area south of Rome was also where the Berlin Christmas market attacker, Anis Amri, spent about a week in July 2015 after getting out of an Italian prison. There's no indication the two ever crossed paths, Repubblica said, without citing sources.
The French interior minister also said he has ordered an internal investigation into why the Marseille attacker had seven encounters with French police and had no residency papers, but wasn't expelled from the country. His latest arrest was just two days before the stabbing, when he was picked up for shoplifting and released.
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