The terror group said on Tuesday that "a soldier of ISIS" had carried out the Berlin attack.
The ISIS group said that the man shot dead by Italian police near Milan on Friday carried out the deadly truck attack on a Berlin Christmas market.
"The Berlin attacker carried out a new attack against an Italian police patrol in Milan and was killed in an exchange of fire," the ISIS-linked Amaq agency said, referring to the fatal shooting of Anis Amri, the prime suspect in the Berlin attack, by Italian police.
Twelve people were killed when the Polish-registered articulated truck, laden with steel beams, slammed into the crowded holiday market late Monday, smashing wooden stalls and crushing victims.
Amaq said Tuesday that "a soldier of ISIS" had carried out the attack "in response to appeals to target citizens of coalition countries".
Germany is part of a US-led coalition fighting ISIS in Iraq and Syria.
An Italian police officer shot Amri dead near Milan's Sesto San Giovanni train station on Friday, four days after the attack which had triggered a Europe-wide manhunt.
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