By Sheena McKenzie CNN

(CNN) -- The Berlin Christmas market attack suspect Anis Amri has been killed in Milan, according to Italian state police.

The suspect was killed in a shootout in Sesto San Giovanni -- a district in the northeastern part of the city -- just after 3am local time, Italian police said on their Twitter feed.

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. A policeman was injured in the shootout and is in hospital.

Amri traveled by train from France

Amri arrived in Milan by train from the French region of Savoy, according to Italian news agency ANSA.

The French anti-terrorism prosecutor's spokeswoman, Agnes Thibault Lecuivre, could not confirm the report, telling CNN the investigation was ongoing.

Italian minister thanks 'exceptional' police

Italian Interior Minister Marco Minniti said the man shot was "without any doubt" Berlin terror suspect Anis Amri, in a press conference Friday.

He added that one of the shot police officers, Cristian Morio, was recovering in hospital. A second police agent, Luca Scata, was not harmed.

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 links to Italy

Twelve people were killed and dozens injured when a truck plowed into a busy Christmas market in Berlin Monday.

The suspect Amri entered Italy in February 2011 without any ID and claimed to be a 17-year-old minor, a spokesman for the Italian state police, Mario Viola, told CNN earlier this week.

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.

ISIS links

Amri's fingerprints were found in the cabin of the truck used in Monday's attack, according to Germany's Interior Minister Thomas de Maiziere earlier this week.

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

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