"A soldier of the Islamic State carried out the Berlin operation in response to appeals to target citizens of coalition countries," the IS-linked Amaq news agency said, without identifying the perpetrator.
The claim came shortly after German prosecutors, saying they lacked evidence, released a Pakistani asylum seeker who was the sole suspect in the case, sparking fears of a killer at large.
"We can't rule out that the perpetrator is on the run," Interior Minister Thomas de Maiziere told broadcaster ZDF, adding he was confident there would be "progress" in the inquiry.
The Pakistani was arrested late Monday after he was reportedly seen jumping out of the truck and fleeing the scene.
But officials had expressed growing doubts over whether they had the right suspect in custody.
Berlin's police chief Klaus Kandt earlier warned that "we may have a dangerous criminal in the area", and announced security would be boosted while urging "heightened vigilance".
Federal prosecutors said they had found nothing to link the Pakistani suspect to Germany's deadliest attack in recent memory.
"The forensic tests carried out so far did not provide evidence of the accused's presence during the crimes in the cab of the lorry," the prosecutor's office said.
As attention switched to the manhunt, investigators asked the public to send them any photos and video footage.
Twelve people were killed when the truck tore through the crowd, smashing wooden stalls and crushing victims, in scenes reminiscent of July's deadly attack in the French Riviera city of Nice.
Another 48 people were injured, 24 of whom were released from hospital by late Tuesday.
The mangled truck came to a halt with its windscreen smashed, a trail of destruction and screaming victims in its wake, with Christmas trees toppled on their side.
Chancellor Angela Merkel -- who visited the scene of the carnage for a minute's silence and then joined a memorial service in the adjacent Kaiser Wilhelm Memorial Church -- labelled the deadly rampage a likely "terrorist" attack.
