The man is aged 21 or 23 and known by three different names, according to reports in the daily Allgemeine Zeitung and the Bild newspaper.
Both media outlets said asylum office papers believed to belong to the man were found in the cab of the truck.
German police on Wednesday stepped up their hunt for the driver of a truck that ploughed through a Berlin Christmas market, in a deadly assault claimed by the Islamic State jihadist group.
The sole suspect -- a 23-year-old Pakistani asylum seeker -- was released late Tuesday for lack of evidence, prompting fears of a killer on the loose and further rattling nerves in a shocked country.
"We can't rule out that the perpetrator is on the run," Interior Minister Thomas de Maiziere told public broadcaster ZDF.
Twelve people were killed when the Polish-registered articulated truck, laden with steel beams, slammed into the crowded holiday market on Monday, smashing wooden stalls and crushing victims.
Twenty-four remained in hospital, 14 of whom were seriously injured, according to de Maiziere.
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From left to right, Klaus Kandt, chief of Berlin's police, Ralf Rother, the Public Prosecutor General in Berlin, Holger Muench, President of the Federal Criminal Police Office (BKA) and Peter Frank, the Public Prosecutor General of the Federal Court of Justice, address a press conference in Berlin on December 20, 2016 AFP
The scenes instantly revived nightmarish memories of the July 14 truck assault in the French Riviera city of Nice, where 86 people were killed by a Tunisian Islamist.
The IS-linked Amaq news agency said "a soldier of the Islamic State" carried out the Berlin carnage "in response to appeals to target citizens of coalition countries".
There was no evidence to back the claim, nor was the perpetrator identified.
The attack comes at a sensitive time for Chancellor Angela Merkel who is running for a fourth term in 2017 but has faced strong criticism over her decision last year to open the country's borders to refugees.
The Pakistani man 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, and he denied the charges under repeated questioning.
"We may have a dangerous criminal in the area," Berlin's police chief Klaus Kandt said, adding that security would be boosted while urging "heightened vigilance".
Following the suspect's release, Kandt told ARD television "one or more" perpetrators were believed to be on the run and possibly armed.
Police said they were chasing up more than 500 tips from the public and examining DNA traces found in the cab of the truck.
Images from the aftermath of the rampage showed the mangled truck with its windscreen smashed, a trail of destruction in its wake, while survivors recounted harrowing stories of near misses and bloody carnage.
Germany in mourning
A Polish man, killed with a gunshot, was found on the truck's passenger seat, said de Maiziere. He was believed to be the original driver of the Polish-registered vehicle.
The 37-year-old Pole named Lukasz worked for his cousin Ariel Zurawski's transport company in northern Poland.
An autopsy indicated that the driver was still alive at the time of the attack, the daily Bild reported.
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German Chancellor Angela Merkel, centre, and German Foreign Minister Frank-Walter Steinmeier,left, walk through the Christmas market of the Kaiser-Wilhelm-Gedaechtniskirche (Kaiser Wilhelm Memorial Church), the day after an attack at the nearby Christmas market in central Berlin, on December 20, 2016 AFP
Merkel visited the scene of the carnage for a minute's silence on Tuesday and then joined a memorial service in the adjacent Kaiser Wilhelm Memorial Church.
Mourners placed flowers and candles at the site while German flags flew at half-mast.
Berlin's landmark Brandenburg Gate was lit in the national colours in honour of the victims, and foreign leaders, led by US President Barack Obama, sent their condolences.
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The Brandenburg Gate is seen in the colors of the German flag in Berlin on December 20, 2016 one day after a truck crashed into a Christmas market AFP
Europe has been on high alert for most of 2016, with bloody jihadist attacks striking Paris since last year and Brussels.
In July, 15 people were injured in two attacks in the southern German state of Bavaria committed by asylum seekers and claimed by the Islamic State group.
The arrival of 890,000 refugees last year has polarised Germany, with critics calling the influx a serious security threat.
Opponents were quick to seize on the carnage as proof that Merkel's liberal asylum policy had endangered the country.