"This government is determined not to allow the descendants of the Nazis to poison our social life, to commit crimes, terrorise and undermine the foundations of the country that gave birth to democracy," Antonis Samaras said in a televised address.
The murder early yesterday of popular hip hop artist Pavlos Fyssas, who wrote music under the nickname Killah P, led to mounting calls for a check on the party's activities.
Many experts have argued that current legislation would make it difficult to slap an outright ban on Golden Dawn, a measure that could be challenged as undemocratic after the party picked up over 400,000 votes in the last election.
"The law will be applied and we believe that this will be the conclusion," government spokesman Simos Kedikoglou told Skai television.
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"Starting from the perpetrators, we will (address) the organisation's structure and how it essentially encouraged criminal acts. A simple ban is not enough," Kedikoglou said.
As the Greek press today called for tighter control of Golden Dawn, whose provocative behaviour has escalated in recent months, rights groups faulted the authorities for allowing the group to operate with near-impunity.
"The cold-blooded murder of a citizen by a Golden Dawn supporter must awaken everyone," the liberal newspaper Kathimerini said in an editorial.
"The monster of Nazism kills -- resist", centre-left daily Ethnos urged Greece's mainstream parties.
The calls came a day after police and protesters clashed as thousands demonstrated against far-right extremism.
The 34-year-old, who was laid to rest on Thursday, was fatally stabbed in the working-class Athens district of Keratsini the previous day by a 45-year-old truck driver, George Roupakias, who later allegedly confessed his Golden Dawn affiliation to police.