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Germany's leading Jewish organization is expressing alarm over footage of flag-waving neo-Nazis in self-styled uniforms marching through a town in eastern Germany on May Day, unhindered by police.

The Central Council of Jews said Thursday the march in Plauen by members of The Third Way party "brings back memories of the darkest chapter in German history."

Footage of the march Wednesday prompted widespread outrage in Germany and calls for authorities in the state of Saxony, where far-right sentiment is particularly strong, to step in.

Police in Saxony said the march had been a success from a policing point of view, with no violence.

The Central Council of Jews said "if the Saxony state government is serious about combating right-wing extremism, it must not allow such demonstrations."