The so-called Islamic State has claimed it carried out the attack on a Berlin Christmas market that killed 12 people.
The militant group's AMAQ news agency said: "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."
Meanwhile, Germany's Interior Minister said that investigators are following several leads on the attack.
He said: "We just heard about the supposed claim of responsibility by this so-called Islamic State that is in fact a gang of terrorists. There are several leads that investigators are following now."
The minister added that "nobody will rest until the perpetrator or the perpetrators are caught".
Earlier, a man who was arrested as a suspect in the attack was released from custody.
In a statement, Germany's chief federal prosecutor said: "The investigation up to now did not yield any urgent suspicion against the accused."
The prosecutor's office said the suspect had made extensive statements during a police hearing, but had denied the offence.
Authorities identified the man earlier as a Pakistani asylum-seeker.
"The forensic tests carried out so far did not provide evidence of the accused's presence during the crimes in the cab of the lorry."
Earlier, police had expressed doubts that the man was the actual perpetrator, Die Welt newspaper reported, citing senior security sources.
"We have the wrong man," said a senior police chief. "And therefore a new situation. The true perpetrator is still armed, at large and can cause fresh damage," the paper quoted the source as saying.
Berlin police said on Twitter that they were being vigilant as the suspect had denied involvement in the incident, which police have said was a deliberate attack.
"The temporary arrested suspect denies the offence," Berlin police tweeted in English. "Therefore we are particularly alert. Please be also alert," they urged the public.
Police said that the man found dead in the truck was a Polish citizen who had been shot.
German Chancellor Angela Merkel has said the whole country is united in mourning after the attack, which also left 48 people injured.
Ms Merkel, who visited the scene, said it must be assumed that it was a terrorist attack.
This is a very difficult day, she said, adding that she is disappointed, shocked and very sad about what happened.
It would be particularly repugnant, she said, if the perpetrator was someone who got protection in Germany as a refugee.
US President Barack Obama has phoned Ms Merkel to offer assistance and condolences following the attack.
Berlin police said that investigators assume that the driver intentionally drove into the crowd of people gathered around wooden huts serving mulled wine and sausages at the foot of the Kaiser Wilhelm memorial church yesterday evening.
Police have taken the Polish registered truck for a forensic examination.
The incident evoked memories of an attack in Nice in France last 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 attack was claimed by the so-called Islamic State.
The interior minister of the German state of Saarland, Klaus Bouillon, has said that Germany is in a state of war.
"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."
France is under a "high level of threat" from terror attack following the carnage in Berlin, President Francois Hollande has said.
Mr Hollande said although France faced an elevated threat, it also already had a large-scale "security operation" in place following a string of jihadist outrages in the country over the past two years.
President Michael D Higgins and Taoiseach Enda Kennyhave both condemned the attack.
In a statement, Mr Higgins said: "The events of the last 48 hours that have included the killing of citizens at a Christmas market in Berlin, an attack on a place of prayer in Zürich and the killing of the Russian ambassador at a public event in Ankara are, as other attacks before, calculated to sow fear at the heart of our societies.
"As President of Ireland I wish to convey my condolences to the families of the victims of these acts and the solidarity of the people of Ireland with all those affected by the violence.
"I wish all the survivors and their communities strength and confidence in these difficult times."
Mr Kenny described the attack as "barbaric".
The Department of Foreign Affairs has said there are no reports of any Irish people caught up in the incident. It said it is continuing to monitor the situation.
Anyone concerned about relatives or friends in Berlin should call 01-4082000.