Berlin man hunt: Police tracking Tunisian suspect

German police are looking for a Tunisian man after finding an identity document under the driver's seat of the truck that ploughed into a Christmas market on Monday killing 12 people, according to Der Spiegel.

Der Spiegel, a German news magazine, said the document was in the name of Anis A, born in Tataouine in 1992. The suspect is also believed to go by two false names, it added. The BBC said police have not commented.

German authorities are still scrambling to pinpoint those responsible for the truck attack on Monday.

One suspect, a Pakistani asylum-seeker who was known to German police, was released Tuesday due to a lack of evidence, and residents have been urged to remain on guard.

ISIS claimed credit Tuesday afternoon for the attack, confirming what German and US officials had presumed was an act of terrorism. The group's Amaq news agency declared the perpetrator to be an ISIS soldier who "executed the operation in response to calls to target nationals of the coalition countries."

Investigators remain "highly alarmed" at the lack of leads in the case, and are wading through witness descriptions and surveillance footage and ramping up efforts to process forensic evidence such as the bloodstains found inside the truck, according to The Washington Post.

The truck ran into the market outside the Kaiser Wilhelm Memorial Church in the Charlottenburg neighbourhood of Berlin at about 8 p.m. local time on Monday. It ploughed through stalls and tables and travelled 50 to 80 metres, according to the Berliner Morgenpost.

A Polish man, named as Lukasz Urban, was found dead in the passenger side of the truck. Germany's interior minister, Thomas de Maizière, confirmed that the man was shot with a shotgun but the weapon had not been recovered. The man was identified by a cousin who owned the truck company where the man had been a driver.