Police released the only detained suspect on Tuesday, saying there was no evidence to link him to the attack.
They now say more than one suspect may be on the run, possibly armed, and security has been stepped up in the German capital.
So-called Islamic State (IS) said one of its militants carried out the attack, but offered no evidence.
The former suspect, a Pakistani national named Naved B, had denied any connection with the attack.
Police said there were no forensic clues to link him to the vehicle, and had expressed doubt about his involvement soon after his arrest.
After his release, police officials admitted that those responsible may still be at large.
"No-one will rest until the perpetrator or perpetrators have been caught," Interior Minister Thomas de Maiziere told German media.
Berlin Mayor Michael Mueller said security had been increased, with extra police and barriers in place at markets to prevent copycat attacks.
"The right thing is to keep your eyes open - be vigilant in this situation. But you can move around safely in public places. There is no need for panic," he said.
IS had claimed responsibility for the attack through its self-styled Amaq news agency, saying one of its "soldiers" had carried out the attack "in response to calls to target nationals of the coalition countries".
However, IS offered no proof, and did not identify the attacker. Federal prosecutor Peter Frank told reporters that the style of attack and the choice of target suggested Islamic extremism.
But Mr de Maiziere reacted cautiously to the claim, saying "several lines of investigation" were being pursued.
The attack took place at the Breitscheidplatz Christmas market in Berlin, where the lorry was driven through the crowd and several stalls for a distance of 80 metres (87 yards) .
In addition to the 12 dead, 49 people were injured. At least a dozen remain in critical condition.
The lorry's original driver, Polish citizen Lukasz Urban, was found dead on the passenger seat, reportedly with gunshot and stab wounds to his body. No gun was recovered.
Monday's incident mirrored the lorry attack on Bastille Day crowds in the French city of Nice on 14 July, which was also claimed by IS.
Both IS and al-Qaeda have urged their followers to use vehicles as a means to attack crowds.
A vigil was held on Tuesday evening at the Kaiser Wilhelm Memorial Church, next to the scene of the tragedy.
German Chancellor Angela Merkel, whose "open door" policy on migrants has been criticised by her opponents, acknowledged fears that the attacker could be one of them.
"I know that it would be particularly difficult for us all to bear if it turned out that the person who committed this act was someone who had sought protection and asylum in Germany," she said.
But she vowed to punish those responsible for the attack "as harshly as the law requires".
Her political opponents, including the far-right Alternative fur Deutschland (AfD), have criticised her over the attack, saying she has compromised Germany's security by letting migrants in without sufficient checks.