A gun fired at police in Milan by the man suspected of attacking a Christmas market in Berlin last month was the same one used to kill the driver of the truck that ploughed into revellers in the German capital, Italian police have said.

Anis Amri, a failed asylum seeker from Tunisia, was shot dead in a gunfight with police in the Milan suburb of Sesto San Giovanni on 23 December, days after he allegedly killed 12 people in Berlin.

Amri is also suspected of shooting dead a truck driver in Germany and hijacking his vehicle, which he then drove into the Christmas market crowd.

Police had been carrying out tests to ascertain if the same gun was used in both the Berlin and Milan shootings.

"The comparison carried out between the exploded cartridge from the terrorist's weapon in Sesto and the one found by the German police has given unequivocal proof that they were fired from the same gun," police said in a statement.