Almost 1,200 migrants - some crammed onto overcrowded inflatable dinghies - have been picked up by Greek authorities in the eastern Aegean Sea in the past two days.
Packed boats were being towed on to the shores of Kos yesterday, with refugees dropping to their knees to pray after completing the perilous journey.
One woman even stopped to take a selfie on her mobile phone after the boat in which she had travelled was apprehended by coastguards on its way from Turkey.
Boats containing dozens of migrants have also been taken to the Greek islands of Lesbos, Chios and Farmakonisi in recent days.
After Italy, financially crippled Greece is the main destination for refugees, mostly from war-ravaged Syria plus economic migrants seeking a better life in the EU. About 30,000 have already arrived this year.
On the holiday island of Kos, some of the new arrivals - mainly Syrians and Afghans - are staying in a deserted hotel.
Kos, which is only 25 miles long and five miles wide, is of particular concern to the authorities, with many people-trafficking boats able to land without detection.
Despite being under Greek control, most of the Aegean islands are closer to Turkey, with Kos just two miles from Bodrum. Journeys from the port take as little as 20 minutes, with migrants paying smugglers up to 800 euros (£565) each for a place on a boat.
While some traffickers carry out several journeys a day, other migrants land on inflatable dinghies that are discarded on the island’s pristine beaches. A police station built to hold only 36 people has become a refugee camp after more than 200 migrants with nowhere else to sleep were packed in. Dozens settled in the building’s courtyard, living in filthy and cramped conditions.
The influx will fuel fears that Greece could unleash a wave of economic migrants to travel to Britain and the rest of Europe.
Greek politicians have threatened to hand travel papers to vast numbers of people, including 10,000 migrants held in detention centres, in the row over EU austerity measures. The country’s proximity to Turkey, regarded as a key buffer in the fight against Islamic State encroaching into Europe, has prompted concern that jihadis could use the route.
It is also feared that some of the people trafficking gangs are linked to IS, with smuggling fees used to fund the group’s terrorism