Islamic State claimed responsibility for an attack in which a truck plowed into crowds in a Christmas market and killed 12 people.
"The executor of the operation.. in Berlin is a soldier of the Islamic state and he executed the operation in response to calls to target nationals of the coalition countries," the militant group's AMAQ news agency said on Tuesday.
German authorities on Tuesday released a Pakistani asylum-seeker arrested after the crash due to a lack of evidence and the interior minister said the real perpetrator may still be on the run.
The truck smashed into wooden huts serving mulled wine and sausages on Monday evening at the foot of the Kaiser Wilhelm memorial church, one of west Berlin's most famous landmarks. Forty-five people were injured, 30 severely.
The Chief Federal Prosecutor's Office said in a statement it had been unable to prove that the suspect had been in the cabin of the truck at the time of the attack and said he had denied any involvement.
Earlier, Die Welt newspaper quoted an unnamed police chief as saying: "We have the wrong man. And therefore a new situation. The true perpetrator is still armed, at large and can cause fresh damage."
Commenting on the suspect's release on Tuesday evening, German Interior Minister Thomas de Maiziere told ZDF television: "That's why it is true that one cannot rule out that the perpetrator is still at large."
He said there was still no doubt the Berlin incident had been an attack but the motive remained unclear. He also said it was not yet known how many foreigners were among the victims of the attack, adding that no children had been among the dead.
News of the arrest of the 23-year-old Pakistani had led politicians in Germany and beyond to demand a crackdown on immigration, but Chancellor Angela Merkel urged caution.
"There is much we still do not know with sufficient certainty but we must, as things stand now, assume it was a terrorist attack," she told reporters earlier on Tuesday.
"I know it would be especially hard for us all to bear if it were confirmed that the person who committed this act was someone who sought protection and asylum," she added.
The truck belonged to a Polish freight company and its rightful driver was found shot dead in the vehicle. The Polish truck driver had arrived hours earlier in the German capital and spoken to his wife about 3 p.m., according to his cousin.
When she called again an hour later, there was no answer.
"At 3.45 p.m. you can see the movement on the GPS (Global Positioning System). The car moved forward and back. As if someone was learning to drive it," said the cousin, Ariel Zurawski, who was also the boss of the trucking company.
"I knew something was wrong."
Merkel joined hundreds of mourners on Tuesday evening at a memorial service at the church near the site of the attack. Her spokesman said she had spoken with the leaders of seven European countries and also with President Barack Obama, who all assured her of their support for Germany.
Security officials in Germany and Europe have warned for years that Christmas markets could present an easy target for militant attacks. In 2000, an al-Qaeda plan to bomb the Strasbourg Christmas market on New Year's Eve was foiled.
There were no concrete barricades at the Berlin Christmas market, as have been installed at a similar venue in Britain.
The attack fueled immediate demands for a change to Merkel's immigration policies, under which more than a million people fleeing conflict and poverty in the Middle East, Africa and elsewhere have arrived in Germany this year and last.
"We must say that we are in a state of war, although some people, who always only want to see good, do not want to see this," said Klaus Bouillon, interior minister of the state of Saarland and a member of Merkel's Christian Democrats (CDU).
Horst Seehofer, leader of the CDU's Bavarian sister party, said: "We owe it to the victims, to those affected and to the whole population to rethink our immigration and security policy and to change it."
'FEAR OF EVIL'
The record influx has hit Merkel's ratings as she prepares to run for a fourth term next year and has boosted support for the anti-immigrant Alternative for Germany (AfD).
AfD leader Frauke Petry said Germany was no longer safe and "radical Islamic terrorism has struck in the heart of Germany."
The incident evoked memories of an attack in Nice, France in July when a Tunisian-born man drove a 19-tonne truck along the beach front, mowing down people who had gathered to watch the fireworks on Bastille Day, killing 86 people. That was claimed by Islamic State.
The influx of migrants to the European Union has deeply divided its 28 members and fueled the rise of populist anti-immigration movements that hope to capitalize on public concerns next year in elections in France, Germany and the Netherlands.
On Tuesday morning, investigators removed the black truck from the site for forensic examination. People left flowers at the scene and notes, one of which read: "Keep on living, Berliners!" One woman was crying as she stopped by the flowers.
Merkel said Germans must not be cowed by the attack: "We do not want to live paralyzed by the fear of evil."
"Even if it is difficult in these hours, we will find the strength for the life we want to live in Germany - free, together and open."
Other European countries said they were reviewing security.
Austrian Interior Minister Wolfgang Sobotka called for biometric and fingerprint checks to be introduced along the Balkan route used by many migrants arriving in Europe in order to better control foreign jihadist fighters' movements.
London police said they were reviewing their plans for protecting public events over the festive period.
Manfred Weber, head of the center-right European People's Party, said: "It's not an attack on a country; it's an attack on our way of life, on the free society in which we are allowed to live."