Following its unprecedented election to parliament, Greece's neo-Nazi group Golden Dawn has been engaged in 'law and order' crackdowns and solidarity gestures that have boosted its popularity, alarming the state.

In recent weeks the once-fringe group has organised Greeks-only food handouts and blood donations, and has twice ousted migrant peddlers from street markets to the delight of local operators and the outrage of authorities.

Tightly regimented and dressed in black T-shirts stamped with the meander, an ancient Greek motif, Golden Dawn is also suspected of orchestrating a rising trend of racist violence against foreigners, legal or otherwise.

And it has sent squads of black-clad supporters to harass and intimidate political opponents at public events.

The government has already accused Golden Dawn of attempting to usurp the role of the police and warned that "storm battalions" would not be tolerated, a direct reference to the paramilitary gangs that helped Adolf Hitler's rise to power.

Public Order Minister Nikos Dendias earlier this month stripped the group's 18 lawmakers of their police guards after one of them was allegedly implicated in the smashing of immigrant trading stalls.

Golden Dawn retorted that it was fully entitled to help merchants and traders brought low by the crisis and accused the government of "taking the side of smugglers and illegal migrants."

The group's ratings have risen to over 10 percent in recent opinion polls.

"They seek to appear as the upholders of the law" to a nation groaning under a third year of austerity measures and decades of political corruption, criminologist Sophia Vidali told AFP.

"It's a strategy reminiscent of Italian neo-fascism in the '70s," she said. The self-styled nationalist party, which campaigned in June elections with pledges to "scour the country clean", has capitalised on the perception that undocumented migration has been allowed to run rampant.

It has benefited from judicial inertia and a suspiciously soft-handed response by police, who usually fail to arrest Golden Dawn members even when under direct attack by them.

And it has exploited anger towards Greece's political system which is blamed by most people for the country's economic ills.

"It's a new phenomenon that is very dangerous for the parliamentary system," said Yiannis Mavris, a political analyst whose polling institute Public Issue recently recorded the party's rating at "nearly double" its score at the last election, where it picked up over 425,000 votes.

Golden Dawn "is here to stay," Mavris said.

A former police unionist who is now a lawmaker recently warned the ruling coalition that planned pay cuts to police "would send 300,000 families directly to Golden Dawn."

And a former police minister last year revealed that Golden Dawn militants had carried out "joint actions and assisted Greek police."

Dimitris Psaras, a journalist investigating far-right groups, says Golden Dawn has links with German neo-Nazis.

"They are trying to appear as the only credible response to the system," he said, deploring the state's slow-paced response.

So far, the government has been forced to tread with caution as the party usually sends its lawmakers -- who can only be prosecuted by special permission from parliament -- to head street operations.

The Supreme Court has duly called on parliament to lift the immunity of three Golden Dawn lawmakers who were present at the market peddler crackdowns.

Three far-right militants -- one of them a former Golden Dawn political candidate -- are set to go to trial next week after seven deferrals, accused of stabbing Afghan migrants.

But Justice Minister Antonis Roupakiotis has warned that it will take more than legal action to stop the "inhuman" behaviour of Golden Dawn members.

"We are wrong if we believe that the Golden Dawn phenomenon can be addressed with legislation. We must seek the causes of this Nazi, fascist and inhuman behaviour by Golden Dawn members," said Roupakiotis.

Rights activists see little room for an anti-racist campaign of substance, as the conservative-led government is itself raising the tone against migrants.

Prime Minister Antonis Samaras has pledged to crack down on undocumented migration which he termed "an unarmed invasion" during the election campaign.