Deutsche Welle reported that suspected members of Reichsbuerger group were allegedly planning attacks on police officers, asylum-seekers and Jews.
About 200 officers were involved in the operation.
The federal prosecutor's office said the raids targeted six people accused of founding the group.
A seventh person is suspected of helping obtain supplies for them, including arms and ammunition.
The 12 raids took place in Baden-Wuerttemberg, Berlin, Brandenburg, Lower Saxony, Rhineland-Palatinate and Saxony-Anhalt.
No details of any arrests have been released.
A statement from the prosecutor's office said: "The goal of today's search measures was to obtain further evidence of the actual creation of a formal group, as well as the alleged planned criminal acts and any potential tools."
The suspects were largely connected via social media, said Deutsche Welle, and were believed to have begun planning armed attacks in spring 2016.
However, the news website said investigators had not found "concrete" evidence pointing to a terror attack.
The Reichsbuerger ("Reich Citizens") group does not recognise the authority of the post-war German federal republic.
It believes in the continued existence of a German empire, or Reich, dating back to 1937 or even earlier.
Bavarian officials said the group's ideology was "nationalist and anti-Semitic... clearly extreme right".
Police have raided a dozen apartments across Germany in an operation to arrest right-wing extremists plotting attacks, federal prosecutors say.