also "announced an act of revenge against Germans because they were standing in the way of Islam".
It earlier emerged that the 27-year-old Syrian was facing deportation to Bulgaria, a German interior ministry spokesman said.
"Syrians cannot at the moment be deported to Syria, but that doesn't mean that Syrians overall cannot be deported," Tobias Plate told a regular government news conference.
"The Syrian in Ansbach was facing deportation and this was to Bulgaria," he said.
The man was denied asylum in Germany a year ago.
He blew himself up outside the festival in the country's fourth violent attack on members of the public in less than a week.
A spokeswoman for the Bavarian state police force said it was unclear whether the man was an Islamist militant, and that investigations were continuing.
A government spokeswoman told the same news conference that it was too early to decide on changes to Germany's refugee policy before the results of the investigation into the attack were published.
"The acts of the last days and weeks do not show a uniform picture," said Ulrike Demmer. "Most terrorists who carried out attacks in Europe over the last months were not refugees."
German newspaper Die Welt quoted Bavarian Interior Minister Joachim Herrmann earlier as saying: "My personal view is that it is unfortunately very likely that a real Islamist suicide attack took place here."
Last night’s incident, on top of three other attacks since 18 July that left ten people dead and 34 injured, will fuel growing public unease about Chancellor Angela Merkel's open-door refugee policy.
More than a million migrants have entered Germany over the past year, many fleeing war in Afghanistan, Syria and Iraq.
Police said three of the 12 wounded were in a serious condition after the attack in Ansbach, a town of 40,000 people southwest of Nuremberg that has a US Army base.
The dead man had been in treatment after twice before trying to kill himself, though yesterday’s explosion was more than just "a pure suicide attempt", Mr Herrmann told Reuters.
An Islamist link could not be ruled out, he told reporters earlier.