Greece's prime minister has vowed to rein in the neo-Nazi Golden Dawn party after one of the group's members murdered a prominent anti-fascist singer, sparking national outrage.

Popular hip-hop artist Pavlos Fyssas was fatally stabbed in the working-class Athens district of Keratsini by a 45-year-old truck driver who allegedly confessed he was affiliated with the Golden Dawn.

The death of Fyssas, 34, who wrote music under the name Killah P, has sparked fresh calls for investigations into the organisations activities.

The victim's family said that Fyssas and a small group of friends were ambushed by a large gang of Golden Dawn supporters outside a cafeteria.

In a televised address, Greece's prime minister Antonis Samaras described the group as Nazis.

"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," he said.

The liberal newspaper Kathimerini wrote in an editorial that there must be zero tolerance to the criminal activity of the Golden Dawn.

"The cold-blooded murder of a citizen by a Golden Dawn supporter must awaken everyone," it said.

The centre-left daily Ethnos urged Greece's mainstream parties to resist "the monster of Nazism".

The calls came a day after police and protesters clashed as thousands demonstrated against fascism and rights groups criticised authorities for allowing the group to operate with near-impunity.

The Hellenic League for Human Rights said that the neo-Nazi group's acts of violence were escalating "with impunity, as a rule".

"The stance of Greek authorities betrays tolerance or distance owing to fear," the league said.

Unrest coincides with latest wave of strikes over austerity measures

The killing came amid the latest wave of anti-austerity strikes in Greece, with thousands also out in the streets on Wednesday to protest against reforms the government has agreed to undertake in return for international bailout funds.

Following news of the murder, those demonstrations quickly morphed into protests against fascism, with police firing tear gas at protesters in Athens, the northern city of Thessaloniki and the western city of Patras.

Protesters clash with riot police in Athens on Wednesday. ( Reuters: Yannis Behrakis )

Many experts have argued that current legislation would make it difficult to slap an outright ban on Golden Dawn.

Greece's police minister, Nikos Dendias, said the government would toughen legislation on organised criminal activity to rein in Golden Dawn, which has been implicated in migrant beatings and attacks on rival party members.

Just days before Fyssas's killing, members of the Communist party were assaulted by alleged Golden Dawn supporters whilst putting up posters.

Golden Dawn has repeatedly denied involvement in the incidents and its ratings have steadily risen in a country weary of austerity and political corruption.

The party currently ranks third in opinion polls, its popularity undiminished by the disruption of political events and a recent attempted assault on Athens mayor George Kaminis by one of its politicians.

The Golden Dawn's spokesman, Ilias Kasidiaris, was recently acquitted of aiding an assault on a left-wing student in 2007.

He now faces another trial for striking a Communist lawmaker during a 2012 talk show.

AFP