The group, 12 of whom were detained on Friday, wanted to attack Muslim places of worship during prayers, Der Spiegel magazine and the daily Bild said.
They planned to imitate the attacks in Christchurch in New Zealand in which 51 people were killed at two mosques and intended to use semi-automatic weapons, CNA reported.
The alleged leader of the group, which was known to the authorities and had been under observation, had detailed his plans at a meeting organized with his accomplices last week.
Investigators learned about it from someone who had infiltrated the group, the two publications said.
Investigators launched the raids to determine whether the suspects already had weapons or other supplies that could be used in an attack.
German authorities have turned increased attention to the country's underground extreme right scene since the murder of conservative local politician Walter Luebcke last June and an October attack on a synagogue in eastern city Halle.