Some 12,700 Germans are inclined towards violence, of an estimated 24,000 far-right extremists, according to interior ministry figures.
Hundreds of flag-waving extremists caused alarm this week when they marched through an eastern town.
Germany’s main Jewish organisation said the march should not have been allowed. The marchers carried a banner that read “social justice instead of criminal foreigners”. They carried flares and banged drums through the centre of Plauen, a town in Saxony whose synagogue was burnt down by the Nazis in November 1938.
The Saxony march took place on Wednesday, on the eve of Jewish remembrance of the Holocaust. Leaders of the left-wing Linke party in Saxony said they were appalled that “uniformed Nazis were allowed to march with torches and drums”.
Germany has seen a rise in support for the far right, with the Alternative for Germany party now the largest opposition party in the Bundestag. But other, more extreme groups have emerged, with more than half of their members prone to violence according to the interior ministry, which provided figures in response to a request from the liberal FDP party.
Hundreds of websites and social media channels, including messaging services and video platforms, were being screened by the authorities for far-right propaganda, the ministry said. It said the extreme right “creates platforms on which the scene is active and exchanges its propaganda and seeks to spread it”.
FDP spokesman Konstantin Kuhle told the Neue Osnabrücker Zeitung that new ideas and better skills were needed to combat radicalisation on the internet.
The eastern state of Saxony in particular has been fertile ground for the far right. Germany’s Central Council of Jews said that if the state government was serious about tackling the extreme right it would ban such marches.