When the man was asked for his papers, he pulled a .22 calibre gun out of his backpack and fired, police said.
The driver of the police car returned fire, killing the suspect. One policeman was injured in the shootout and is in hospital.
In a press conference Friday, Italian Interior Minister Marco Minniti said the man shot was Amri “without any doubt.” He added that one of the shot police officers, Cristian Morio, was recovering in hospital. A second police agent, Luca Scata, was unharmed.
The Interior Minister also thanked the “exceptional” Italian police forces, saying that they immediately identified and “neutralised” Amri.
Italian Prime Minister Paolo Gentiloni had informed German Chancellor Angela Merkel about the shootout earlier in the day, he said at a press conference Friday.
Amri ‘traveled from France’
Italian news agency ANSA said Amri arrived in Milan by train from the French region of Savoy.
The French anti-terrorism prosecutor’s spokeswoman, Agnes Thibault Lecuivre, could not confirm the report, telling CNN the investigation was ongoing.
If true, it would mean that Amri passed through at least two European borders after fleeing Berlin after the attack on the market outside the Kaiser Wilhelm Memorial Church in Berlin on Monday evening. Twelve people were killed and dozens injured when a truck plowed into the market.
Links to Italy
While in Italy, he served four years in prison after he was involved in an arson attack on a school, his father told Tunisian radio.
Viola said that Amri’s jail term for damaging state property, assault and arson at the Lampedusa refugee center began in late 2011. He was released in May 2015.
Italian authorities ordered his deportation, but Tunisian authorities wouldn’t accept the request on the grounds of a lack of proper documentation, Viola said.
At that point, Italian authorities told Amri to leave the country, and officials lost track of him.
Amri was “not suspected” of terrorism at the time and was considered a “petty criminal,” Viola said. The Tunisian came to Italy at the same time as thousands of others amid the turmoil of the Arab Spring, he said.
He left for Germany more than a year ago, according to his father.
The 24-year-old had been at large since Monday’s attack, and European authorities had offered a reward of up to 100,000 euros (about $104,000) for information on his whereabouts.
According to German investigative files obtained by CNN on Thursday, Amri had ties to an ISIS recruitment network in Germany and had previously discussed launching an attack there.
Amri and several members of the so-called Abu Walaa network backpacked more than 10 miles in Germany to get into shape as they prepared to travel to join ISIS, a police informant inside the network told investigators, according to investigative files obtained by CNN.
CNN’s Richard Greene, Lorenzo D’Agostino, Livia Borghese, Margot Haddad, Joshua Berlinger and Laura Smith-Spark contributed to this report