The mystery over the migrant-turned-suspect in Tunisia's Bardo Museum massacre intensified Thursday amid questions about his alleged involvement and his movements in Italy after arriving with a boat full of rescued refugees a month before the attack.

As Italian officials defended their handling of Abdelmajid Touil, indications pointed to his presence in Italy in the days before and after the March 18 massacre. The mayor of Trezzano sul Naviglio, Fabio Bottero, said Touil is listed as having been present at his twice-weekly Italian lessons March 16 and March 19.

Touil, a 22-year-old Moroccan, was arrested on Tuesday on a Tunisian arrest warrant at the home of his mother in Gaggiano, near Milan, on accusations that he helped plan and execute the attack, which killed 22 people. Tunisian officials have said he provided "indirect" support to those responsible. The extremist Islamic State group claimed responsibility for the attack.

Interior Minister Angelino Alfano insisted before Parliament on Thursday that there were no terrorism-related concerns about Touil when he arrived in Sicily Feb. 17 with about 90 other migrants who had been rescued at sea. His comments were aimed at defusing criticism from anti-immigrant politicians that Islamic extremists were slipping into Italy via migrant boats to plot attacks.

Alfano said Touil was fingerprinted and photographed, as is routine for newly arrived migrants — identifications that then helped police positively identify him when they arrested him Tuesday. He had been ordered expelled, as is routine, but authorities lost all trace of him until Tuesday.

At the time he arrived in Italy, "Touil was not considered even at the potential level as a terrorist, much less a dangerous subject for the security of our country," Alfano said.

Only after the attack did Tunisia identify him as a potential suspect. Alfano also suggested that independent of Tunisia's investigations, Italian intelligence had also begun tracking Touil as a potential suspect.

Italian news reports have said that Touil didn't pray at any mosque and that not even a Quran was found in the search of his home Tuesday. Alfano said two pen drives, a cell phone and some personal items were taken.

Alfano said that after his arrest, Touil consented to having DNA taken, an indication that Italian authorities want to be certain that he is indeed the Touil sought by Tunisia.

Italian media report Alfano as saying that the country remains on high alert.

The spokesman of Tunisia's Interior Ministry, Mohammed Ali Aroui, would not comment on Touil's whereabouts the day of the attack but said he was certain about his identity.

"For us, he is the one we are looking for and we continue coordinating with the Italians for his extradition," Aroui told The Associated Press on Thursday in Tunis.

Touil's mother, Fatima, meanwhile, has denied her son's involvement. In comments reported by Corriere della Sera and other newspapers, she said her son watched TV footage with her of the Bardo attack and that he had not left Gaggiano since the day he arrived.

"On March 18 he was in the apartment in Gaggiano," she said in comments reported by Corriere.

Police have said the only indication they had from the family before the arrest came in mid-April after his mother reported her son's passport missing.