The man who drove his van into a crowd in western Germany on Saturday was a German citizen with psychological problems and with ties to far-right groups, local media reported on Sunday.
German public television ZDF said police identified the attacker as 49-year-old Jens R, who shot himself dead after the crash.
The attacker had ties to far-right groups, but whether it played a role in the attack was unclear, ZDF reported, citing unnamed security sources.
Two people were killed and more than 20 others injured on Saturday after the attacker rammed his van into people sitting outside a restaurant in the northern German city of Munster.
Attacker stored gas bottles and canisters
Authorities said the attacker had stored several gas bottles and canisters with gasoline and bio-ethanol at his home.
Police said they have found a deactivated Kalashnikov assault rifle and party firecrackers at the house of the attacker in Munster.
But authorities could not yet determine the exact motive for the attack.
"So far, we have not found any evidence of political motivation behind this attack," chief prosecutor Elke Adomeit told reporters on Sunday.
Muenster Police President Hajo Kuhlisch said, "We are now focusing our investigations on getting a comprehensive picture of the perpetrator's behavior in the weeks (before the crash) to find out his motivation for this horrible act."
Soon after the violent attack, Germany's far-right politicians blamed it on refugees, and shared anti-immigrant and Islamophobic messages on social media.
Raids on far-right movement
Germany's federal prosecutor's office said on Sunday that special forces have raided apartments across the country in connection with allegations that at least eight people were involved in creating a far-right terrorist organisation.
The prosecutor's office said the raids were targeting members of the far-right Reichsbuerger movement that does not accept the rules of today's Germany, but identifies with the state system of the German Kaiserreich area from 1871-1918.
Authorities searched homes in Berlin, Brandenburg and the eastern state of Thuringia on suspicions that the accused started forming an organisation last year at the latest.
Authorities were also investigating the killings of some people and say the group may have procured weapons to enforce their goals.
The prosecutor's statement said no one was detained during the raids.