Berlin truck terrorist Anis Amri has been shot dead in Milan after attacking a police officer who asked him for ID.

Amri "immediately" produced a gun when approached by police and shot an officer during a routine patrol in the northern Italian city early on Friday.

The Tunisian was then killed, and there is "absolutely no doubt" that the man was Amri, Italian interior minister Marco Minniti said.

Amri, 24, was suspected of driving a truck into crowds at a Christmas market in Berlin on Monday, killing 12 people and injuring 48.

At a press conference on Friday morning, Mr Minniti said: "One of our police officers on patrol stopped a person who was just walking around looking very suspect. And the moment he was stopped, the man, without hesitating, he immediately took his gun and shot at the police officer who asked him for his identification papers."

He added: "Police officers reacted to the shootout. The person who attacked our police officer was killed."

Mr Minniti said: "There is absolutely no doubt that the person who was killed is Anis Amri, the suspect of the terrorist attack in Berlin."

He said the officer who was shot, Cristian Movio, is recovering in hospital, adding that he has thanked him and wished him a happy Christmas.

"I told him that I hope he gets better soon. The boy is very motivated. He's an extraordinary person. I thank him for the professionalism that he demonstrated, for the professionalism that him alongside his colleague had demonstrated," he said.

The other officer involved was Luca Scata, the press conference heard.

Although the minister declined to disclose many operational details, he said the moment - which took place at 3am - demonstrated the excellence of Italy's security services.

He said: "I would like to thank the whole of the security of our country. Italy should be really proud of our security, full stop, and I repeat - really proud, full stop."

Mr Minniti added: "As soon as this person entered our country he was the most wanted man in Europe and we immediately identified him and neutralised him and this means our security is working really well."

The minister said: "We are talking about an operation that happened at three in the morning in the middle of a really important city centre and it happened in complete security.

"The only problem was for the police officer who was shot - no-one else was injured."

Police said Amri travelled from Chambery in France to Turin in Italy, then on to Milan's Central Station where he arrived at 1am, and then on to Sesto San Giovanni.

Earlier this week, relatives of Amri urged him to turn himself in to police.

The suspect, who turned 24 on Thursday, is understood to have left Tunisia after the 2011 Arab Spring uprising and spent time in Italy before entering Germany last year.

His asylum claim was rejected and authorities identified him as a threat before the Berlin attack.

His brother, Abdelkader Amri, had previously told the Associated Press: "I ask him to turn himself in to the police. If it is proved that he is involved, we dissociate ourselves from it."

German authorities issued a wanted notice for Amri on Wednesday and offered a reward of up to 100,000 euro (£85,000) for information leading to his arrest.

According to the Corriere della Sera website, Mr Scata's mother, who was not named in the report, said: "Being in the police has always been his dream. Luca is strong and determined and we are proud of him."

His father Giuseppe said: "He is a courageous lad, he did his duty."

Former Ukip leader Nigel Farage said Amri's apparent ability to travel from Germany to Italy showed that the Schengen system - which allows border-free movement between 26 European states - is "a risk to public safety" and should be scrapped.

"If the man shot in Milan is the Berlin killer, then the Schengen area is proven to be a risk to public safety," said Mr Farage. "It must go."

Ukip immigration spokesman John Bickley said: "It gives no-one in Ukip any pleasure whatsoever to state 'we warned you'. Nigel Farage made it patently clear earlier this year that Isis would use the refugee crisis and Merkel's 'open door invite' to the Middle East to smuggle hundreds of jihadists into Europe.

"The slaughter of innocents in Paris and Nice was no coincidence and the latest atrocity in Berlin shows that Isis is now at war with Europe.

"The EU's continued support of Schengen and uncontrolled immigration both within and from outside the EU is both costing innocent lives, leaving hundreds with life-threatening or life-changing injuries and undermining social cohesion and our Judeo-Christian culture."

According to La Repubblica, Mr Scata is from Siracusa province in Sicily, and studied for two years at Catania.

It adds that in 2011 he did a year in the army as a volunteer and went on to qualify for the police, but is still waiting for his first official permanent posting.

La Repubblica said Mr Movio is from Latisana, near Udine, and has been in the police since 2008, adding that he also served in the army in an Alpine regiment in Venzone.