Locked in a sunbaked football stadium without food or water, about a thousand refugees have queued for hours to register with overwhelmed Greek authorities on the holiday island of Kos.

The island is now at the forefront of a humanitarian crisis sweeping the financially broken country.

Inside the stadium, three police clerks were struggling to register hundreds of refugees, and for the second day used fire extinguishers to control the jostling crowd. An estimated 300 travel documents were handed out by early afternoon.

"The situation here is very bad and police here they beat a boy, they beat a man, they beat children, it's too bad," Syrian refugee Laith Saleh, who is in the stadium, said. "We can't go out."

Representatives of Doctors Without Borders, the medical charity also known as Medecins sans Frontieres (MSF) which is working on Kos, deplored the conditions in the stadium, where most refugees were sent after being evicted from makeshift camps all around the town.

"What we see now is a completely disproportionate focus on security management of these people without the relative humanitarian assistance that they need," MSF's Vangelis Orfanoudakis said.

"There are just two toilets, no access to water, they now have put a water hose for all the people. The situation is really dramatic," he said.

Greece is the main gateway to Europe for tens of thousands of refugees and economic migrants, mainly Syrians fleeing war, as fighting in Libya has made the alternative route from north Africa to Italy increasingly dangerous.

Nearly 130,000 people have arrived since January on the eastern Aegean Sea islands from nearby Turkey - a 750 per cent increase over last year.

Tourism-reliant Kos, which received 7,000 migrants last month and has seen tourist arrivals drop about seven per cent this year, is a stark study in contrasts.

Boatloads of refugees arrive in the rosy hues of dawn - as the last revellers straggle out of night clubs and joggers run along the seafront. Huge yachts and cruise ships anchor just off the detention centre, refugees sleep on bicycle lanes forcing cyclists to swerve, and bikini-clad tourists strolled past a man clad in traditional Iraqi dress.

Scores of Syrians landed early on Wednesday, crossing the 2.5 mile strait from Turkey in rubber boats - which, in many cases, local men rush to carry away for their own use.

"I feel good to be here, but I still miss my family" in Syria, said Omar Mohammad, a 25-year-old English literature graduate from Aleppo.

He said the three-hour crossing from Turkey was his third attempt to reach Greece in four days. On two previous occasions, Turkish officials had prevented him from leaving.

Unlike during past immigration crises in Greece since the early 1990s, the refugees do not want to stay. Their destinations are wealthy countries such as Germany or the Netherlands, and all they seek from Greece is temporary travel papers to continue their trek through the Balkans and central Europe.

So they end up in the old stadium or outside - on the beachfront, in tents, under trees, fully clothed adults washing in the shallows as splashing children play with the life-vests from their sea crossing.

Municipal officials have long been lobbying for the refugees to be taken to the mainland. Mayor Giorgos Kyritsis has pledged to get them off parks and public areas.

MSF's Julia Kourafa said some refugees had fainted from exhaustion or hunger in the stadium. Hundreds were seen climbing the 12-foot perimeter wall to go and buy food, and one man was taken away in an ambulance after he fell and seriously injured his leg.

Some refugees set up tents in the little shade available, while MSF teams were planning to erect awnings.

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