The mayor's office in Athens is poised for a major stand-off over food handouts in Syntagma square on Thursday after the far-right Golden Dawn party vowed to press ahead with the distribution of Easter treats to "Greeks only" amid mounting European pressure for the group to be outlawed.

Pledging to defy a ban by the capital's mayor, the extremists said they would go ahead with the handout of traditional Orthodox Easter fare, including lamb and eggs, to Greeks afflicted by draconian austerity.

"It is food that is aimed for the thousands of Greek families blighted by the genocidal policies of the memorandum," said the party, referring to the loan agreement Athens has signed with international creditors to keep the debt-crippled country afloat.

The neo-fascist organisation said the event was aimed solely at those Greeks who could not afford to enjoy Easter because of budget cuts and record levels of unemployment.

"Priority will be given to families with three or more children," it said in a statement. "We remind the mayor that in Greece we still have a democracy."

Catapulted into parliament with 18 MPs last June, the ultra-nationalists have seen their support surge by deftly playing on popular dissatisfaction over policies blamed for poverty.

A Hamas-style distribution campaign of food and clothes for the needy has topped the party's outreach programme – and increasingly added to its appeal. Polls show the group now firmly entrenched as Greece's third biggest political force.

The ascent of the far right has embarrassed Greek officials, with the coalition government accused of not doing enough to stem a rise in racially motivated attacks in recent months. Athens' left-leaning mayor Giorgos Kaminis, a progressive on immigration issues, has led the drive to deflect the criticism.

In a statement he said: "We are making it absolutely clear that the city of Athens views the planned gathering tomorrow as illegal and it will do whatever is required for it not to take place."

A similar, Greek-only food drive last year was met with applause and widespread attendance.

Emboldened by their growing popularity, the far-right party have also conducted "Greek only" blood drives around the country and taken, increasingly, to storming state-run hospitals to root out foreign staff.

Last week, protesters who gathered outside a hospital in Tripoli, in the southern Peloponnese, were attacked when they attempted to demonstrate against Golden Dawn members collecting blood. A journalist recording the event was brutally beaten, according to witnesses.

With Greece beginning to convey a semblance of stability after three years at the centre of Europe's great economic crisis – and the country preparing for a bumper tourist season – Prime Minister Antonis Samaras' coalition is keen that Athens' image abroad is not further sullied by supporters of a party whose leadership denies the Holocaust and whose symbol resembles the swastika.

The determination of authorities to stop Thursday's food drive comes on the back of a withering report by the Council of Europe's human rights commissioner, which for the first time raises the prospect of the extremist group being banned.

Using language rarely deployed by a European official, the commissioner, Nils Muiznieks, described Golden Dawn as a "neo-Nazi and violent political party". His 32-page report, compiled after a visit to Greece earlier this year, called for the party to be prohibited under legally binding international human rights conventions signed by the country.

The commissioner said local authorities had the right to curb or sanction individuals who actively support or engage in hate crimes under treaties including the European convention on human rights.

Earlier this year, Human Rights Watch warned that xenophobic violence had reached "alarming proportions" in parts of Greece and accused authorities of failing to do enough to stop the attacks.

Thousands of anti-austerity protesters marked May Day, gathering in front of the sandstone building that houses the Greek parliament in Syntagma square.

In contrast to other demonstrations, the protests were peaceful. But the patience of austerity-weary Greeks is wearing thin.

Analysts speak of the risk of unpredictable events shattering the fragile calm. With both Golden Dawn and municipal authorities digging in their heels, officials were tonight praying that Thursday's food drive would not be the trigger.

• This article was amended on 2 May 2013. Nils Muiznieks is the human rights commissioner for the Council of Europe, not for the European Union. This has been corrected.