Greece has long been Europe's main entry point for illegal immigrants from Asia and Africa seeking a better life in the West.
However, its severe economic problems and high unemployment are making the problem worse than ever.
Around 6000 people were detained over the weekend in Athens in a massive operation named after the ancient Greek god of hospitality, Zeus Xenios.
Officers across the city stopped mostly African and Asian people in the street for identification checks. Most were only briefly detained, but about 1600 were arrested for illegally entering Greece and sent to holding centres pending deportation.
Left-wing opposition parties criticised the crackdown, while the Office of the United Nations High Commissioner for Refugees voiced concern migrants from war-torn countries and genuine asylum- seekers could be denied the right of protection.
Some 100,000 illegal immigrants are estimated to enter into Greece every year, mostly from neighbouring Turkey, and up to one million are believed to live in Greece, which has an official population of about 10 million.
The uncontrolled influx contributed to the rise of extreme-right political party Golden Dawn, which gained nearly 7% of the vote in parliamentary elections six weeks ago.
Public Order Minister Nikos Dendias said: "The country is being lost.
"What is happening now is [Greece's] greatest invasion ever. Since the Dorian invasion some 3000 years ago, the country has never received such a flow of immigration."