A private citizen had asked the court to exclude Golden Dawn because its leadership was under investigation over a string of attacks on immigrants and opponents.
Golden Dawn is expected to do well amid a wave of anger over economic austerity – the price Greeks have paid for bailouts totalling €240 billion (£195bn) from the European Union and International Monetary Fund to save the country from a debt crisis.
It is running between third and fifth in opinion polls, and a strong showing would pose a challenge to the fragile coalition government.
The party sports a swastika-like symbol and its members have been seen giving Nazi-style salutes. Golden Dawn, which rejects the label neo-Nazi, entered parliament for the first time in 2012, tapping into resentment over illegal immigrants and mass unemployment. The jobless rate in Greece still stands at nearly 28 per cent.
The investigation into Golden Dawn was triggered by the arrest in September of a party supporter who confessed to the fatal stabbing of an anti-fascist Greek musician.
Golden Dawn leader Nikolaos Michaloliakos is one of six party MPs in jail pending trial. Their arrests followed the killing of the musician.
Two men suspected of links with Golden Dawn have been jailed for life in Greece over the fatal stabbing of a Pakistani immigrant last year.
None of the party’s 18 MPs is on the election list for the European polls on 25 May. Its candidates include two retired senior army officers.
Party spokesman Ilias Kasidiaris, who is running for Athens mayor, is free on bail pending trial on charges of participating in a criminal group.
The government has resisted calls to ban Golden Dawn outright, which would require a constitutional amendment.
Having lived through decades of authoritarian government after the Second World War, including a seven-year military dictatorship, Greece now bars only convicted criminals from contesting elections.
Last year, most of the 154 recorded racist attacks in Greece were attributed to Golden Dawn members, as were most of the 104 so far this year. Many describe Golden Dawn as “neo-Nazi” but the party insists it does not embrace Nazi ideology.
Swedish premier Fredrik Reinfeldt warned last week that Europe’s failure to deliver economic growth and jobs had frayed public trust in democracy and fostered a nationalist climate that could reward anti- immigration, Eurosceptic parties in the EU elections.
He told how he also saw nationalism shaping Russia’s actions in Ukraine, which he said was creating “instability”.
Citizens in the 28 EU countries will vote for 751 members of the European Parliament. Opinion polls suggest an influx of between 150 to 200 Eurosceptic politicians bent on reversing decades of EU integration.
Parties campaigning to limit immigration are expected to do well in a number of countries, including Britain, France and Hungary.
According to a profile of Golden Dawn in Greece’s centre-left daily Ta Nea, Mr Michaloliakos organised the party “along military lines, with him as leader, as the supreme authority”.
He is said to have taken his inspiration from leaders of the 1967-74 Greek junta, whom he reportedly met while serving prison sentences in the 1970s for paramilitary activities.
Golden Dawn may officially deny being neo-Nazi, but its badge resembles a swastika and some of its senior members have praised Adolf Hitler. Mr Michaloliakos himself has denied the existence of gas chambers and crematoria at the site of the Auschwitz death camp.
The party’s political breakthrough came when Mr Michaloliakos won a seat on Athens city council in 2010.
It fought the 2012 general elections on a twin platform, opposing immigration and condemning the bailouts.
As far back as the 1990s, Golden Dawn members were suspected of street attacks on foreigners, according to a profile in another Greek newspaper, Kathimerini.