German prosecutors announced on Monday that they were opening an investigation into the killing of a German tourist in the French capital over the weekend.
The suspected terror attack took place close to the Eiffel Tower in central Paris.
Federal German prosecutors in the German city of Karlsruhe said that they were considering charging the suspected attacker.
He is being investigated on suspicion of being a member of a terrorist organization abroad, as well as for murder.
The investigation will run alongside a French probe being carried out by anti-terror prosecutors.
The assailant attacked a German couple with a knife near the Quai de Grenelle on Saturday. A 23-year-old man was killed, while his companion was injured.
French Interior Minister Gerald Darmanin said the suspect had then tried to attack two more people with a hammer while running from the police.
The suspect was already known to French authorities. He had reportedly pledged allegiance to the so-called "Islamic State" (IS) in a video on social media.
He had also been under close psychological surveillance for mental health issues.
Darmanin told French broadcaster BFM TV on Monday that there had been a "clear failure" in the psychiatric care of the suspect who had been suffering from "an acute mental illness."
ab/nm (AFP, dpa)