A hunt is under way across Europe for Anis Amri, 24, as Germany reels from its worst attack in decades.
"We can report today that we have new information that the suspect is with high probability really the perpetrator," Interior Minister Thomas de Maiziere told reporters on Thursday.
"In the cab, in the driving cabin, fingerprints were found and there is additional evidence that supports this," he said.
Frauke Koehler, a spokeswoman for the federal prosecutor's office, told reporters: "At this point in the investigation, we assume Anis Amri drove the truck."
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Police had carried out searches across Germany on Thursday but made no arrests, she said.
A video clip from a car-mounted dashcam obtained exclusively by Reuters appears to show the truck driving into the market at speed, immediately after which people run away from the scene.
Chancellor Angela Merkel, facing demands to take a much tougher line on immigration and security, said she hoped the perpetrator would be arrested soon.
Islamic State has claimed responsibility for the attack, in which the truck mowed through a crowd of people and bulldozed wooden huts selling Christmas gifts and snacks beside a famous church in west Berlin.
One of the 12 dead was the Polish driver from whom the truck had been hijacked. His body, stabbed and shot, was found in the cab.
Amri had been identified by security agencies as a potential threat and rejected for asylum, but authorities had not managed to deport him because of missing identity documents.
In Tunisia, two of Amri's brothers, Walid and Abdelkader, said they feared the failed asylum-seeker may have been radicalised by radical Islamists while he spent almost four years behind bars in Italy.
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