Police in Germany say there are “no clues” pointing to a possible motive for Saturday’s van attack in Muenster.
They are investigating “all possible avenues”, said the north-western city’s senior prosecutor, Martin Botzenhardt.
On Saturday authorities all but ruled out any Islamist connections for the suspect, a German citizen who shot and killed himself.
Police also identified the two victims killed in the incident as a 51-year-old woman and a 65-year-old man.
The woman was from near Lueneburg in the north of the country, while the man was from Borken near Muenster.
What do we know about the perpetrator?
Mr Botzenhardt said the investigation so far suggested that the driver was “probably” a 48-year-old man from Munich.
“So far there are no indications of a possible background for the crime,” he said. “The investigations are being conducted at full speed and on all fronts.”
Although officials have provided few details, the German newspaper Frankfurter Allgemeine Zeitung is reporting that the man lived just 2km (1.2 miles) from the restaurant.
The public broadcaster ZDF suggested he had links with far-right extremists, but said he was not known to be one himself. The report said police were searching his apartment.
German media reports also said the man had mental health problems – something state authorities have not confirmed or denied.
How did the incident unfold?
A vehicle, reportedly a grey VW van, was driven into a restaurant terrace area at 15:27 local time (13:27 GMT) on Saturday.
Eyewitnesses said it was driven at speed and photographs of the aftermath showed tables and chairs strewn across the popular tourist square.
An employee at one of the cafes told local media that she heard a bang and people screaming.
“I’m angry – it’s cowardly to do something like this,” she told German television channel N24.
Daniel Kollenberg, who witnessed the aftermath, told the BBC: “I think it is a deliberate attack because it’s not allowed for cars to go in this area.”
He added: “People are calm, but really shocked.” The city, in Germany’s north west, has a population of about 300,000.
Chancellor Angela Merkel said in a statement that she was “deeply shaken” by the incident.
“Everything possible is now being done to clarify the facts and to support the victims and their relatives,” she said.
French President Emmanuel Macron tweeted in French and German, saying his country was suffering with Germany.
The incident comes at a time of a heightened concern in Europe, following a spate of jihadist attacks using vehicles to kill pedestrians in the UK, France and Sweden.
Local police repeatedly urged people on Saturday afternoon not to speculate about the nature of the incident and wait for official information.
Germany has seen a number of jihadist attacks in recent years. In December 2016 a lorry was driven into a crowd at a Christmas market in the capital, Berlin.
The attacker who hijacked the vehicle, Tunisian asylum seeker Anis Amri, was shot dead in Italy four days later.