Police in the Greek island of Kos have beaten migrants with batons and sprayed them with fire extinguishers as hundreds were gathering at a football stadium to wait for immigration documents.

An AFP reporter at the scene on Tuesday said the officers were apparently trying to prevent a stampede as a crowd tried to squeeze through a door into the stadium.

At least one woman had already fainted in the heat and many children were crying as the tightly packed group of people jostled for space, just days after the country's handling of migrants came under fire from the UN.

The migrants, many of whom had fled conflict in Syria and Afghanistan, had been camping alongside the island's roads, beaches and in parks for weeks.

Tensions on the tourist island were high with its mayor warning on Tuesday that the refugee crisis could end in "bloodshed", claiming there were 7,000 migrants stranded in Kos, which has a population of only 30,000 locals.

Kos mayor Giorgos Kiritsis told the Greek ANA news agency there "was a risk of bloodshed if the situation degenerates" further.

An officer in Kos was suspended on Monday after being filmed slapping and shoving migrants queueing outside the local police station as they waited to be documented so they could go to Athens, the country's capital.

On Tuesday, hundreds of protesting migrants calling for quicker registration began blocking the main coastal road in the island's main town, staging a sit-in.

"We want papers, we want to eat", they chanted.

'Totally shameful'

Kos is one of several Greek islands that has seen a recent surge in of migrant and refugee arrivals.

Greek Prime Minister Alexis Tsipras last week said the refugee crisis "surpasses" his crisis-hit nation's resources and called for European Union assistance.

The UN refugee agency's division for Europe said last week that 124,000 refugees and migrants have landed in Greece since the beginning of the year.

The agency said that Athens' response to the problem had so far been "totally shameful", with many of those landing on the eastern Aegean islands near Turkey usually forced to sleep in the open, lacking access to washing facilities and toilets.

Greek authorities are converting a container facility near central Athens to accommodate hundreds of migrants currently sleeping in one of the capital's parks.