12 people were injured in the blast outside a bar in the city of Ansbach
The suspected Ansbach bar bomber had violent videos, including one on his phone, pledging allegiance to the leader of Islamic State, according to officials.
Police say the 27-year-old had enough materials to build another bomb.
Joachim Herrmann, Bavaria's interior minister, said an initial translation of the video suggested the man had intended a "revenge" attack against Germany.
Mr Herrmann said the video strongly suggested the bombing had been a "terrorist attack".
The Syrian man, who had been denied asylum in Germany, killed himself and injured 12 others, three seriously, in an explosion outside a wine bar in the German city.
Security officials say he detonated an explosive device after being turned away from a music festival being attended by thousands of people because he didn't have a ticket.
Mr Herrmann said the contents of his backpack had the potential to kill and injure many more victims as they included both explosives and metal parts.
A spokesman for Germany's interior ministry said the danger of an attack remained high, and security is reported to have been increased at airports and train stations.
"Due to the situation in Syria, he was not deported. In spite of the rejected application, he was given exceptional leave to remain," Mr Herrmann said.
Interior ministry spokesman Tobias Plate said there had been a continued intention to deport the suspected bomber.
"Syrians cannot be deported to Syria at the moment, but that doesn't mean that Syrians overall cannot be deported," he said at a news conference.
"The Syrian in Ansbach was facing deportation and this was to Bulgaria" (where he had first submitted a request for asylum).
Mr Plate said the suspect had received two deportation notices, most recently on 13 July.
The suspect was known to the authorities and had repeatedly received psychiatric treatment, including for attempted suicide.
"We don't know if this man planned on suicide or if he had the intention of killing others," Mr Herrmann said.
"My personal view is that I unfortunately think it's very likely this really was an Islamist suicide attack," he earlier told German news agency dpa.
"The obvious intention to kill more people indicates an Islamist connection."
After the attack, a large-scale operation involving 200 police and 350 rescue workers was launched, and a helicopter brought in.
Armed police have raided a building used to house asylum seekers three kilometres from the scene.
Detectives have asked anyone with mobile phone footage to send it in.
This man saw the explosion.
Witness Thomas Debinski said: "People were definitely panicking. The rumour we were hearing immediately was that there had been a gas explosion.
"But then people came past and said it was a rucksack that had exploded. Someone blew themselves up.
"After what just happened in Munich, it's very disturbing to think what can happen so close to you in such a small town."
More than 2,000 people were evacuated from the nearby festival.
Germany has been on high alert following a series of incidents in recent days.
On Sunday, a Syrian refugee wielding a machete killed a woman and injured two other people in the German city of Reutlingen. The 21-year-old man was apparently acting alone and has been arrested.
And on Friday, nine people were killed in a shooting near a shopping centre in Munich, which was carried out by an 18-year-old who later turned the gun on himself.