Greek police have arrested 18 migrants following a fire at a refugee camp on the island of Lesbos, the Athens-based newspaper Kathimerini reported Tuesday.

Fighting, and then later a fire, broke out at the overcrowded Moria camp on Monday evening, forcing the more than 3,000 residents to flee and scatter across the island following a weekend of protests by both islanders and residents at the site.

The arrested men from Afghanistan, Cameroon, Senegal and Syria are suspected of starting the fire and of fighting inside and outside the so-called refugee reception "hot spot" on the island.

A least nine of them will face arraignment before a custodial judge, the report said.

More than 60 per cent of the camp is believed to have been destroyed in the fire.

Mayor Spyros Galinos has warned the situation could escalate again at any time.

"Given the overcrowded camp, it was only a matter of time before it happened. If the situation is not immediately defused, we will surely experience, new, even worse incidents," Galinos said.

Camp occupants on the island have been demanding for some time to be allowed to travel to the Greek mainland, to escape overcrowded conditions in the Moria camp.

The situation on the island is uncertain, with thousands of migrants now homeless and barred from the Greek mainland. The migrants are due to be returned to Turkey as part of a deal struck in March between the European Union and Ankara to deter further migrants from risking the sea journey to Europe.

The Greek government did not comment on the Lesbos situation on Tuesday. Prime Minister Alexis Tsipras and members of the Greek government are currently in New York attending the UN refugee summit.

Mayor Galinos accused the government of letting down Lesbos and the other island communities bearing the brunt of the refugee crisis.

"It cannot be that only some 15 communities in the whole of Greece shoulder the whole refugee problem," he said.

European Commission spokeswoman Natasha Bertaud said she had been informed by the Greek authorities that "most of the migrants evacuated for security reasons have now been returned to the camp."

"And we've also been informed by the Greek authorities that they're now taking measures to restore the damages in the camp," she said.

"Of course, we as the commission continue to provide full assistance to the Greek authorities in this and the management of the refugee crisis more generally," Bertaud said.

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