A Europe-wide manhunt is under way for the 24-year-old.
Before entering Germany, Anis Amri, 24, had served four years for arson in Italy.
A European arrest warrant was issued after Anis Amri’s residence permit was found in the cab of the truck that left a trail of carnage at the market near west Berlin’s most famous shopping street, the Kurfuerstendamm.
German authorities warn Anis Amri could be armed and dangerous and are offering a reward of up to €100,000 ($104,000) for information leading to his arrest.
It is thought he may have been injured in a struggle with the Polish driver of the truck, found murdered in the cab.
On December 22 there were reports of police raids in Dortmund. Two apartments were searched and four people arrested, local media reported.
Anis Amri was reported by the Ruhrnachrihten news website to have lived in Dortmund from time to time. Residents at one block of flats recognized him from photos and said he had spent time with a German of Serbian origin who was detained last month on suspicion of supporting ISIS, Ruhrnachrichten said.
German Chancellor Angela Merkel has met her security cabinet to discuss the investigation into the attack.
A police notice lists six different aliases used by Anis Amri, born on 22 December 1992, who at times tried to pass himself off as an Egyptian or Lebanese.
The suspect was facing deportation as of June but there was a delay in receiving paperwork from Tunisia.
A brother of the suspect in Tunisia, Abdelkader Amri, told AFP he could not believe his eyes when he saw his relative’s face in the media.
“I’m in shock and can’t believe it’s him who committed this crime,” he said, before adding: “If he’s guilty, he deserves every condemnation.”
An earlier suspect, a Pakistani asylum seeker, was freed from German custody on December 20, after officials admitted they had the wrong man.
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