A German far-right party, the NPD, has threatened to mount street patrols to "protect" areas where it claims the police are not doing enough to stop crime by asylum-seekers.
An NPD video on Facebook purports to show one such patrol in Bavaria, but officials played down its significance.
Vigilantes can be prosecuted, depending on how they act.
The NPD warning follows alleged assaults by four asylum-seekers on Saturday in Amberg, northern Bavaria.
In eastern Germany an office of the Alternative for Germany (AfD), another far-right party, was damaged by an explosion on Thursday night. The attack, in the town of Döbeln, did not injure anyone.
In 2017, the AfD entered the German parliament (Bundestag) for the first time, winning 94 seats.
The NPD (National Democratic Party of Germany) is smaller and has only won seats in regional assemblies. It is widely seen as neo-Nazi and there have been several attempts to ban it. It has an MEP in Brussels, Udo Voigt.
The young Amberg asylum-seekers are now in custody, suspected of injuring 12 people with kicks and punches. Bavarian broadcaster BR says an injured 17-year-old was admitted to hospital.
The four - believed to be two Afghans, a Syrian and an Iranian - were reportedly drunk at the time.
The NPD organiser for the Nuremberg region, Axel Michaelis, told the BBC that his party had "launched the 'Create Protection Zones' initiative six months ago... so that our presence will give citizens a better sense of security in especially crime-affected urban areas".
"The protection zone in Amberg and elsewhere will make the police deploy in more numbers, and that will already be an achievement," he said.
"The police are overwhelmed. Officers are doing their best, but criminality, especially by asylum-seekers, has got out of hand," he said.
Amberg police told the BBC that there was no evidence so far of NPD patrols in the town, but they were investigating the party's claims. "There is no far-right scene in Amberg," police spokesman Hans-Peter Klinge said.
In an interview with Spiegelonline (in German), Amberg's centre-right mayor Michael Cerny spoke of "an overblown reaction" to Saturday's violence.
He accused the NPD of trying to exploit the situation politically. "Now they want to discredit the police's work... but the police have done a good job," he said.
Shock of Chemnitz
There was alarm in Germany last August when far-right activists launched a wave of protests in the eastern city of Chemnitz, after the death of a Cuban-German man in a brawl with migrants.
Some of the far-right militants clashed with police. There were also counter-demonstrations by leftist groups.
In western Germany a 50-year-old man is in custody, suspected of racially-motivated attempted murder, after ramming his car into groups of foreigners on New Year's Eve.
Nine people, including women and children, were injured in Bottrop and Essen, in Germany's industrial Ruhr region. A Syrian woman needed life-saving surgery.
The German suspect, named only as Andreas N, has a history of mental illness, reports say. The Süddeutsche Zeitung daily says (in German) he has admitted deliberately targeting foreigners.