Two senior Greek police officials have quit their jobs in a shake-up after the murder of an anti-fascist musician by an alleged member of neo-Nazi party, Golden Dawn, sparked protests, and led to a probe of a possible police connection.

Police said two regional supervisors for southern and central Greece had stepped down on Monday as an inquiry was under way into possible links between the police department and the Golden Dawn.

The police shake-up also involved the suspension of a number of senior officers on the island of Evia for failing to investigate a Golden Dawn office, located near a local police station, where weapons were allegedly kept.

The department's internal affairs division was also tasked with determining whether officers had participated in illegal Golden Dawn activities.

About 30 such incidents are under investigation, a police source told the AFP news agency.

At the same time, nearly a dozen senior officers switched posts, including the heads of the anti-terrorist squad, the organised crime squad and the guns and explosives squad, police said.

The fatal stabbing of 34-year-old musician Pavlos Fyssas on September 18 touched off street protests and prompted authorities to take a harder stance against Golden Dawn.

The neo-Nazi party has already been linked to assaults on immigrants although it officially denies such attacks, while several of its lawmakers have also been involved in violent incidents and have yet to face justice.

The head of the World Jewish Congress, Ronald Lauder, said Greece had a "moral obligation" to act.

"There can be no legitimate place in the Greek parliament for parties whose public statements and actions are racist or anti-Semitic and who operate in many ways like the Nazis did 70 years ago," Lauder said in a statement, also calling for tougher legislation.

Three Golden Dawn lawmakers are to be tried for smashing up the street stalls of migrant peddlers in two separate incident.

Another member of parliament, party spokesman Ilias Kasidiaris, is also due in the dock for striking a female Communist MP during a talk show last year.

Rise of Golden Dawn

Observers however voiced scepticism about the scope of the police shake-up.

"There is an outcry and that is why they are doing this," Sophia Vidali, a criminologist at the University of Thrace, told AFP news agency.

She added that it was "not about the senior officers alone, we know there is an issue with the rank-and-file officers, entire stations might have to change", she said.

Migrant groups have repeatedly complained of police apathy when reporting racist beatings.

Capitalising on a rise in social tension in the debt-stricken country, Golden Dawn was first elected to parliament last year with nearly seven percent of the vote, winning 18 seats out of an overall 300.

It further boosted its popularity by organising food handouts and blood donations exclusively for Greeks.

The government is now trying to find a way to deal with the neo-Nazi party, which so far has benefitted from a law granting elected MPs immunity from prosecution.

The musician's killer, 45-year-old truck driver George Roupakias, has confessed to the crime but claims he was acting in self-defence.

He has been charged with voluntary manslaughter and illegal possession of a weapon.

Fyssas, who wrote music under the nickname Killah P, was fatally stabbed outside a cafe in the working-class Athens district of Keratsini.

Golden Dawn quickly denied links with the alleged killer, but pictures soon surfaced of Roupakias participating in party activities and members of his family reportedly worked for the organisation.