The government ordered an investigation into Golden Dawn's activities after Fyssas' death, with the case being handled by Greece's Supreme Court and anti-terrorist squad under organized crime laws.
Separately, Health Minister Adonis Georgiadis said Wednesday that authorities were also investigating reports that a psychiatrist at Athens' main state psychiatric hospital had been granting certificates for gun licenses to Golden Dawn members without conducting the required tests, and that the psychiatrist had been calling for the military to take up arms against the government.
The crackdown against Golden Dawn has included raids on party offices and supporters suspected of being involved in attacks.
Police said Wednesday they arrested a 34-year-old in Crete after a raid on his house uncovered a replica gun, a military-style knife and a collapsible metal baton. Golden Dawn membership cards and other paraphernalia with the party logo were also found.
Golden Dawn, whose senior members have expressed admiration for Adolf Hitler although they deny being neo-Nazi, won nearly 7 percent in 2012 general elections and holds 18 seats in the country's 300-member Parliament.
Its members and supporters have frequently been suspected of carrying out violent attacks, mainly against immigrants. The party had appeared to grow bolder in recent weeks, with alleged actions taking on a more political, rather than racist hue. Earlier this month, party supporters were accused of attacking Communist party members putting up posters in a district west of Athens, leaving nine requiring hospital treatment.
Despite its reputation for violence, the party had enjoyed growing popularity as poverty has risen in Greece. But Fyssas' death the first killing attributed to political motives and allegedly involving the party appears to have dented its appeal.
Recent opinion polls show drops in popularity in recent days, although it is still the third most popular party in Greece.
A poll conducted by the Alco company for the news website Newsit published Wednesday showed support for Golden Dawn sliding to 6.8 percent after last Wednesday's killing, compared to 10.8 percent in a similar poll in June.
The poll was conducted by telephone interviews of 1,000 people nationwide. It didn't provide a margin of error.
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Costas Kantouris in Thessaloniki contributed to this report.