German investigators are searching for the killer or killers involved in the attack on a crowded Christmas market in Berlin after a man arrested soon after the rampage was released due to lack of evidence and the Islamic State group claimed responsibility.

Police in the capital said they had received 508 tips about Monday's attack as of Tuesday night, but it was not clear whether prosecutors had any concrete leads.

Twelve people were killed and 48 others injured when a lorry was driven into the crowds at the market next to the Kaiser Wilhelm Memorial Church in the centre of the city.

Shortly afterwards, a Pakistani man who had gone to Germany as an asylum-seeker, was detained based on a description from witnesses of a suspect who jumped from the truck and fled.

However, he was freed on Tuesday after prosecutors were unable to find any evidence linking him to the attack.

The claim of responsibility carried on IS's Amaq news agency on Tuesday described the man seen fleeing from the truck as "a soldier of the Islamic State" who "carried out the attack in response to calls for targeting citizens of the Crusader coalition".

Germany's top prosecutor, Peter Frank, told reporters before the claim that the attack was reminiscent of July's deadly truck rampage in Nice in the south of France and appeared to follow instructions published by IS.

"We don't know for sure whether it was one or several perpetrators," he said. "We don't know for sure whether he, or they, had support."

Berlin Mayor Michael Mueller said on Wednesday that it was "good to see that Berliners aren't being intimidated".

"I don't think there's any need to be afraid," he told ZDF television. "The police presence has been significantly heightened ... and of course other measures taken to find the perpetrator quickly."

Mr Mueller argued that there are limits to increasing security, given the number of public spaces and events.

"It wouldn't be our free and open life any more if we escalated security measures so much that people worry about going anywhere, that there are strict entry checks," he said. "We don't want that. It must be appropriate and goal-oriented."

Referring to security measures, he added: "A lot has happened, and more certainly will."

Sign up to our free newsletters

Get the best updates straight to your inbox:
Please select at least one mailing list.

You can unsubscribe at any time by clicking the link in the footer of our emails. We use Mailchimp as our marketing platform. By subscribing, you acknowledge that your information will be transferred to Mailchimp for processing.