The suspect, 25-year-old Anis Hanachi, was arrested Saturday on an worldwide warrant issued by France while riding a bicycle in the northern city of Ferrara, authorities told reporters in Rome.
He is suspected of complicity in the Marseilles attack, in which two young women were stabbed to death, and of radicalizing his brother.
The attacker, Ahmed Hanachi, had been married to an Italian woman and lived in Aprilia, south of Rome, from about 2006 to 2014.
"Anis was flagged as a risky individual who probably had been a foreign fighter" in Iraq and Syria, Claudio Galzerano, director of an Italian anti-terrorism police squad, told reporters.
Police are now investigating Anis's possible contacts in Italy.
Swiss federal police said the brother of Hannachi they had detained was known to foreign police forces for links with the "jihadist terrorist movement", though it was unclear what role, if any, the suspect played in the Marseille attack.
Anis Hannachi, the brother of Marseilles killer Ahmed Hannachi, combatted with jihadi foreign fighters in Syria, according to information the French authorities passed on to their Italian counterparts, investigators said Monday.
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La Canfora's original story was referenced by a few outlets, including the Associated Press (AP), who later issued a correction . The president told the crowd at the rally on September 22 that teams should fire players who kneel during the anthem.
Ms Maret said they were arrested at the migrant registration centre in Chiasso.
"A hypothesis that remains to be verified is that it was him who indoctrinated his brother Ahmed and caused his radicalization", Giannini said.
Another one of his brothers and a sister were detained in Tunisia late last week and had been questioned by anti-terror investigators there.
Swiss police have detained two Tunisians wanted in connection with a deadly knife attack at Marseille train station in France on Oct 1, a source close to the investigation said on Tuesday (Oct 10).
Two Tunisian security officials, speaking on condition of anonymity, said Ahmed and Anouar were suspected of being "extremists".
Their father Noureddine has told AFP that he doubted his sons in Europe had been radicalised, adding that he had not heard from either for two months. The militant Islamic State group claimed responsibility for the attack, but did not name the assailant.