Officials said asylum office papers believed to belong to the Tunisian man with alleged links to the radical Islamist scene were found in the cab of the 40-tonne lorry used in the attack that killed 12 people.
"There is a new suspect we are searching for -- he is a suspect but not necessarily the assailant," Interior Minister Thomas de Maiziere told reporters, saying a Europe-wide search was underway. He declined to give further details.
But his regional counterpart in North Rhine-Westphalia state, Ralf Jaeger, said the man identified as Anis A. or Ahmed A. by media, had already been under investigation for planning an attack.
Counter-terrorism officials had exchanged information about him, most recently in November, and a probe had been launched suspecting he was preparing "a serious act of violence against the state," Jaeger said.
The suspect came to Germany in July 2015 but his application for asylum was rejected this June.
His deportation, however, got caught up in red tape with Tunisia, which long denied he was a citizen. The required documents only arrived on Wednesday, two days after the Berlin attack, said Jaeger.
One conservative lawmaker, Stephan Meyer, said the suspect was being watched by police.
"We are apparently talking about a potentially dangerous suspect who was known to authorities and belonged to the Salafist-Islamist scene," he told reporters after a meeting of parliament's interior affairs committee.
A previous 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.
Twelve people were killed when the Polish-registered articulated truck, laden with steel beams, slammed into the crowded holiday market late Monday, smashing wooden stalls and crushing victims.
The scenes 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.
Twenty-four people remained in hospital, 14 of whom were seriously injured, De Maiziere said.
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.
Germany is part of a US-led coalition fighting IS in Iraq and Syria.
Tunisia is one of the biggest suppliers of jihadist fighters, with some 5,500 of its nationals believed to be involved in combat in Syria, Iraq and Libya.
The attack comes at a delicate 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 case inflamed the debate about asylum policy in general, and in particular the speed at which rejected asylum seekers can be deported.
Germany this year moved to declare Algeria, Morocco and Tunisia as safe countries of origin, to raise the bar for asylum requests after last year's record influx of around 890,000 people.
But the bill has been stuck in the upper house for months over human rights concerns in those countries.
Germany in mourning
A Polish man, killed with a gunshot, was found in the truck's passenger seat. The 37-year-old Pole named Lukasz worked for his cousin Ariel Zurawski's transport company in northern Poland.
Zurawski described him as a "good guy" and said his body showed signs of a struggle with the assailant or assailants including stab marks.
"One person would not have been able to overpower him," Zurawski said of the relative he had grown up with, a heavyset man who weighed in at 120 kilos (265 pounds) and stood 183 centimetres (six feet) tall.
"We could see injuries. His face was bloodied and swollen," he told private news channel TVN 24, referring to a photo he received from Polish police.
An autopsy indicated that the driver was still alive at the time of the attack, the daily Bild reported.
Merkel visited the scene of the carnage for a minute's silence on Tuesday and then joined a service in the adjacent Kaiser Wilhelm Memorial Church.
Mourners placed flowers and candles at the site while German flags flew at half-mast and Berlin's landmark Brandenburg Gate was lit in the national colours in honour of the victims.
Europe has been on high alert for most of 2016, with bloody jihadist attacks striking Paris since last year and Brussels.
In Germany, 15 people were injured in two attacks in July in the southern 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.
Marcus Pretzell of the anti-immigration Alternative for Germany party labelled the Christmas market victims "Merkel's dead".