The Berlin attack suspect has been killed in a shootout with police in Milan.

Anis Amri, a 24-year-old Tunisian, had eluded capture since the attack on Monday that killed 12 people and injured another 48 in the German capital.

Italian interior minister Marco Minniti said during a news conference that the man killed in the shootout was identified as Amri "without a shadow of a doubt".

He was stopped near the train station in the northern Italian city at around 3am (2am Irish time) on Friday.

He pulled out a gun from his backpack "without hesitation" and started firing towards the officers, injuring one of them, Mr Minniti said.

The suspect was then shot and killed.

The injured policeman has been taken to hospital and underwent surgery, but his wounds are not life-threatening. 

Mr Minniti did not release further details of the operation, citing an ongoing investigation.

Italian media reports said Amri shouted "Allahu Akbar", or "God is Great", during the firefight.

He reportedly had a train ticket from France in his pocket.

Amri was identified by his fingerprints.

Authorities in Germany and elsewhere had been hunting for Amri, who is believed to be the driver of the truck that rammed through the crowd of shoppers at the market.

Germany was "relieved" at the reports, interior ministry spokesman Tobias Plate said.

Amri used at least six different names and three nationalities in his travels around Europe.

He went to Italy in 2011 and spent time there, including three and a half years in prison for setting fire to a refugee centre. 

He arrived in Germany late last year and sought asylum, but his bid was rejected. 

He was seen as a potential threat long before the attack this week - and was even kept under covert surveillance for six months this year.

But authorities failed to deport him because he lacked valid identity papers and Tunisia initially denied that he was a citizen.

Amri stayed in Berlin at least for a few hours after the attack, with footage showing him at a mosque in the German capital in the early hours of Friday.

The video, published by German public broadcaster RBB, was taken by police officers on a regular stake-out at the mosque, but  Amri was not a suspect at that time.

When police raided the mosque on Friday, he was gone.

German Federal prosecutors have said that they will continue their investigation to see if Amri had an accomplices.