The Tunisian man suspected of ploughing a truck through a crowded Berlin Christmas market was shot dead by police in Milan, Italy on Friday, ending a four-day manhunt across Europe.

Anis Amri, 24, was killed in a shootout after police stopped him during a routine patrol at around 3 am (0200 GMT) in Sesto San Giovanni, in the northern outskirts of Milan.

When an officer asked for his documents, Amri pulled out a gun and shot him. He was killed when police fired back, Italian Interior Minister Marco Minniti said.

The probe now turns to whether Amri, a failed asylum seeker who had been under investigation by German authorities as a potential terrorist before the attack, had accomplices or a support network, top German prosecutor Peter Frank said.

Holger Muench, the head of Germany's federal criminal police, linked Amri to radical Islamist preacher Abu Walaa, who was arrested in Germany in November, but did not provide details on how the two are connected.

Abu Walaa was the suspected head of a group that recruited for and provided financial and logistical support to extremist Islamic State in Germany.

Italian authorities in identified Amri by matching his fingerprints to those found on the truck, German Interior Minister Thomas de Maiziere said.

German investigators are also trying to determine whether the gun in his possession in Milan was the same weapon used to kill the Polish driver of the hijacked truck, and how Amri had managed to evade police for four days and escape unnoticed to Italy.

Italy's Corriere della Sera newspaper reported that police officers found a ticket for a train from Chambery, in south-eastern France, arriving in Milan at 1 am - just two hours before he was shot dead.

Amri reportedly spent several years in Italy before entering Germany in July 2015.

German authorities said they had initiated deportation proceedings but Tunisia failed to issue the relevant documents. Those documents arrived on Wednesday, two days after the attack.

Police say he drove a large truck laden with steel into a Berlin Christmas market late Monday, killing 12 people and injuring 53.

Merkel was scheduled to speak to Tunisian President Beji Caid Essibsi on Friday about the deportation of failed asylum seekers, a government spokeswoman said.

A Berlin official told a parliamentary committee on Friday that several victims of the attack are still in life-threatening condition.

Andreas Geisel, Berlin's senator of the interior, said that 53 people were injured in the attack, 14 of them "very seriously."

A 23-year-old Pakistani man was detained shortly after the attack near city's landmark Kaiser Wilhelm Memorial Church, on the city's popular Kurfurrstendamm shopping street. He was later released after police said there was no evidence connecting him to the crime.

German authorities had said before the shootout in Milan that they believed Amri was injured and still in Berlin. Raids have been held in locations across Germany over the course of the week, including a refugee homes.