Golden Dawn wants non-Greeks out.
Greek authorities have detained 6,000 illegal immigrants in the country's largest deportation so far, in a drive to fight what an official compared to an "invasion".
Public Order Minister Nikos Dendias defended the crackdown, ironically named after the Greek God of hospitality Zeus Xenios, saying the country's economic plight meant it could not afford an "invasion of immigrants".
He likened the immigrants' wave to the attempts by the Dorians to conquer the country. Greek police said more than 1,600 illegal immigrants will be deported.
"Greece and our existence is under threat," he told SKAI radio "What is happening now is (Greece's) greatest invasion ever. Since the Dorian invasion some 3,000 years ago, the country has never received such a flow of immigration."
The invasion of Greek-speaking Dorian tribes traditionally put an end to the heroic Mycenaean age, although historians believe that the Mycenaean civilization was brought down by financial and social uprisings.
"The immigration problem is maybe even bigger than the financial one," Dendias said, calling the issue a "bomb at the foundations of the society and of the state".
"I am not a magician and I know that I am sitting on an electric chair," he said.
Some 88 illegal immigrants were sent back to Pakistan on Sunday. A police spokesman told the BBC that illegal immigrants without the documentations would be repatriated.
"We do not care about colour, ethnicity or religion of the illegal immigrants," Dendias said. "The only criterion is the observance of laws with full respect, I repeat with full respect, for human rights and the European order."
Left-wing opposition parties criticised the crackdown while far-right Golden Dawn party is likely welcome the move.
Golden Dawn, which saw support jump from 0.46 to 7 percent over three years to gain 21 seats in parliament, is regarded as a neo-Nazi party in Greece.
It has appealed to a growing nationalist backlash against financial screw-tightening demanded by the EU and IMF, which has been balmed for plunging Greece into economic turmoil.
The party's main policy is to get rid of all illegal immigrants.
It recently restricted deliveries of free food only to people who could prove they were Greek.
Organisers asked for ID cards of dozens of people surrounding a delivery truck in Athens' Syntagma Square for a handout.
The unemployed and the people with many children were served first. More than 200 people showed up, according to witnesses.
An estimated 130,000 immigrants arrive in Greece each year. The country accounts for 90 percent of the arrests for unlawful entry into the EU. Greece has an estimated 1 million immigrants in a country with a population of less than 10 million.
It is building a fence on its northern border with Turkey, which it blames for doing little to stop immigrants for entering in the country.
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