"My personal view is that I unfortunately think it's very likely this really was an suicide attack in Ansbach,'' Bavarian interior minister Joachim Herrmann told German news agency DPA.
The 27-year-old Syrian refugee blew himself up after being turned away from an open-air music festival.
Herrmann said the man's request for asylum was rejected a year ago, but he was allowed to remain in Germany because of the strife in Syria.
The unnamed man had repeatedly received psychiatric treatment, including for attempted suicide, Herrmann said.
Asked whether the bomber might have links to the Islamic State (ISIS, ISIL, IS and Daesh )group, Herrmann said that couldn't be ruled out, though there was no concrete evidence for this yet.
"The obvious intention to kill more people indicates an extremism connection,''.
Earlier today, a spokesman for the prosecutor's office in Ansbach said the attacker's motive wasn't clear.
If there is an Islamist link or not is purely speculation at this point,'' said the spokesman, Michael Schrotberger.
Roman Fertinger, the deputy police chief in nearby Nuernberg, said it was likely there would have been more casualties if the man had managed to enter the concert venue.
Three of the 12 victims suffered serious injuries in the blast. The attacker's rucksack had contained sharp bits of metal.
The explosion came as Germany, and the southern state of Bavaria in particular, have been on edge.
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