Italian police shot dead the man believed to be responsible for this week's Berlin Christmas market truck attack, killing him after he pulled a gun on them during a routine check in the early hours of Friday morning.

Key points: Anis Amri was stopped by police patrol car at 3:00am and asked to show ID

Anis Amri was stopped by police patrol car at 3:00am and asked to show ID In return Amri shot one officer and the other officer returned fire, killing him

In return Amri shot one officer and the other officer returned fire, killing him Suspect believed responsible for Berlin Christmas market attack which saw 12 people killed

The suspect — 24-year-old Tunisian Anis Amri — travelled to Italy from France, triggering a spate of criticism from eurosceptics over Europe's open-border Schengen pact.

A police chief said his men had no idea they might be dealing with Amri when they approached him at around 3:00am outside a station in Sesto San Giovanni, a suburb of the northern city of Milan.

Amri is suspected of driving a truck that smashed through a Berlin Christmas market on Monday, killing 12 people and injuring close to 50 others.

German authorities issued a wanted notice and security forces across Europe have been trying to track him down after his fingerprints were found inside the truck.

Militant group Islamic State has claimed responsibility for the attack, and acknowledged the shooting of Amri through its news agency.

Italy's Interior Minister Marco Minniti said after the shootout all the necessary checks were conducted and that "the person killed, without a shadow of a doubt, is Anis Amri".

Germany's top federal prosecutor Peter Frank confirmed the man shot dead was Amri, and said the investigation into the attack would continue to determine if there were any accomplices.

"It's very important for us now to find out whether there was a network of supporters and accomplices, whether there were confidants who helped the sought person to prepare and conduct the attack and to escape," he said.

Shootout started after routine patrol check

Milan police chief Antonio De Iesu told reporters that Amri had arrived in Milan's main railway station from France at around 1:00am and had then travelled to Sesto San Giovanni, where two young policemen approached him because he looked suspicious.

"We had no intelligence that he could be in Milan," Mr De Iesu said.

"They had no perception that it could be him otherwise they would have been much more cautious."

Amri failed to produce any identification so the police requested he empty his pockets and his small backpack. He then pulled a loaded gun from his bag and shot at one of the police officers, lightly wounding him in the shoulder.

Anis Amri was named by the prosecutor's office as the man being sought by authorities. ( Supplied )

The suspect then hid behind a nearby car but the other police officer managed to shoot him, killing him on the spot.

Amri was identified by his fingerprints.

Mr De Iesu said that besides the gun, Amri had been carrying a small pocket knife. He also had a few hundred euros on him but no mobile phone.

Amri once spent four years in jail in Italy and police were trying to work out if he knew someone in Sesto.

A judicial source had earlier said that police had a tip-off that Amri might be in the Milan area and that additional patrols had been sent out to look for him. Mr De Iesu denied that, saying only that the authorities had recently ordered tighter security and more identification checks across the country.

"The two policemen simply decided to check up on a foreigner," De Iesu said.

Meanwhile, the Breitscheidplatz Square marketplace, which has been largely sectioned off since the attack, re-opened to defiant visitors on Thursday night local time.

Visitors lit candles and laid flowers at memorial sites across the square.

Berliners told the ABC they had attended the market to make their city feel more normal again and to show terrorists they will not win.

Christmas markets are a long-held German tradition, and are found all over the country.

The market was closed after Monday's attack, but was re-opened to the public just days before Christmas. ( AP/ DPA: Michael Kappeler )

Reuters