Der Spiegel reported on Thursday that the suspect would be placed in pre-trial detention.
Both the Federal Court of Justice and the Public Prosecutor General’s Office seat in the city of Karlsruhe. The suspect, who was detained by the police after committing the attack, was reportedly flown there by helicopter.
Footage released by the N-TV channel showed the suspect, with a gauze bandage on his neck, exiting the helicopter surrounded by armed security officers.
According to German media reports, the suspect had been injured during his detention.
The attack took place on Wednesday and left two people killed and as many injured, according to the police. There were around 80 people inside the synagogue at the moment of the attack.
German media identified earlier the suspected gunman, arrested by police after the attack, as Stephan Balliet, a 27-year-old neo-Nazi German citizen, who broadcast his attack online.
Justice Minister Christine Lambrecht said on Thursday that the authorities considered the shooting to be an anti-Semitic terror act.