PIRAEUS, Greece—At a dark crossroads here in September, Greek police kept a safe distance while black-clad activists from the fascist movement Golden Dawn chased and attacked Pavlos Fyssas, a 34-year-old rapper.

The police had long been in the habit of standing by while Golden Dawn's paramilitary squads rolled into action, mirroring the hesitance of Greece's political leadership to deal with the growing movement's muscle. Only after a Golden Dawn member fatally stabbed the rapper did police officers make an arrest, according to 15 police and witness depositions.

The arrest was the start of a risky crackdown on a party steeped in street violence and neo-Nazi rhetoric, whose surging support since last year symbolizes how Europe's economic crisis has fueled the Continent's most radical forces. From Spain to Finland, extremes of left and right, regional separatists and antiestablishment populists are on the march. Golden Dawn, once a fringe group known for stiff-arm salutes and Holocaust denial, rose to nearly 15% support in opinion polls by this fall.

Violence in Greece hasn't come only from the far right. On Nov. 1, two men on a stolen motorcycle stopped at a Golden Dawn branch in an Athens suburb and shot two party activists dead. An extreme-left group took responsibility, saying it was revenge for the killing of Mr. Fyssas.

The Golden Dawn crackdown the government is attempting takes the form of an effort to prove it is a "criminal organization" in which membership is a crime, a charge the party denies.