German authorities have conducted raids across the country, seizing explosives and arresting four people accused of founding a right-wing group to attack mosques and housing for asylum seekers.

Police arrested three men and a woman accused of leading the group during raids by some 250 investigators on homes in Saxony and four other states, the federal prosecutor's office said in a statement.

Prosecutors allege the four helped found the "Oldschool Society" (OSS) group and were planning to attack asylum-seeker housing, mosques and well-known members of the Islamic community in Germany.

The four arrested, identified only as Andreas H, 56, Markus W, 39, Denise Vanessa G, 22, and Olaf O, 47, in line with German privacy laws, are being held on terrorism charges and are also accused of having procured explosives.

The statement identified Andreas H and Markus W as the group's president and vice president.

The North Rhine-Westphalia state interior ministry said Olaf O was from the western city of Bochum and had been under observation since November as "a leading member of the OSS".

"According to current investigations, it was the group's goal to conduct attacks in smaller groups inside Germany on well-known Salafists, mosques and asylum-seeker centres," the statement said.

"For this purpose the four arrested procured explosives for possible terror attacks by the group."

Inquiries made by the Associated Press news agency to an apparent cell phone number and email address for the group were not immediately returned.

Attack plans

German Interior Minister Thomas de Maiziere said the Oldschool Society appeared to be a newly formed group.

Rhineland-Palatinate interior minister Roger Lewentz, at the same news conference, held up what appeared to be the group's logo - a white skull on black background framed by bloody butcher's cleavers with lightning bolts resembling the runes of the Nazi SS.

"The SS rune is in there - that's not for nothing," Lewentz said.

Prosecutors said they are still trying to determine whether the group had concrete attack plans and refused to comment beyond their written statement.

There have been conflicts in recent years between far right groups and the Muslim community in North Rhine-Westphalia that have escalated into violent street fights.

In 2013, authorities said they foiled a plot to assassinate a high-ranking member of a far-right party in the state.

Right-wing groups have been a renewed focus for German intelligence agencies after it came to light that a neo-Nazi group calling itself National Socialist Underground, or NSU, allegedly killed eight Turks, a Greek and a policewoman between 2000 and 2007. It is also believed to be behind two bombings and 15 bank robberies.

De Maiziere said statistics released Wednesday showed a sharp increase of 22.9 percent in violent crimes by right-wing extremists in 2014 to 1,029, three times the number in 2013.

Anti-Semitic attacks have also reportedly increased.

The report suggested the rise could be linked to months of non-violent anti-Islam protests by a group calling itself Patriotic Europeans against the Islamisation of the West, or PEGIDA.