The UN refugee agency pulled out staff on Tuesday from facilities on Lesbos and other Greek islands being used to detain refugees as an international deal with Turkey came under further strain.
Greece began arresting everyone arriving in boats from Turkey after the agreement went into effect on Sunday. They are being held at European Union-supervised registration centres known as "hotspots", in what Greek government officials describe as "compulsory supervision".
Under the deal, detained refugees will be sent back to Turkey, which in return will receive additional EU financial aid and join an EU resettlement programme for Syrians and others fleeing war.
The international medical humanitarian organisation Doctors Without Borders (MSF) also said it suspended its activities at the "hotspot" known as Moria on Lesbos island.
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"We made the extremely difficult decision to end our activities in Moria because continuing to work inside would make us complicit in a system we consider to be both unfair and inhumane," said Marie Elisabeth Ingres, MSF head of mission in Greece.
"We will not allow our assistance to be instrumentalised for a mass expulsion operation, and we refuse to be part of a system that has no regard for the humanitarian or protection needs of asylum seekers and migrants."
The UN agency's spokeswoman Melissa Fleming said in Geneva it is "concerned that the EU-Turkey deal is being implemented before the required safeguards are in place in Greece".
"Greece does not have sufficient capacity on the islands for assessing asylum claims, nor the proper conditions to accommodate people decently and safely pending an examination of their cases," said Fleming.
About 2,000 people have been detained since the deal took effect, with refugees still arriving in boats despite the crackdown.
"Clearly we do not believe that, so far, Turkey has implemented what has been agreed. Migration flows are not significantly lower ... that should have happened immediately," Greece's government spokeswoman Olga Gerovasili said.
Greek Prime Minister Alexis Tsipras, she said, telephoned German Chancellor Angela Merkel on Tuesday and urged her to press Turkey to crack down on refugee smugglers.
She said full implementation of the agreement would require preparations for about 10 days.
More than 50,000 refugees and migrants are currently stranded in Greece, with many still camped out at the closed Greek-Macedonia border where protests continued for a third day.
One protester, a young Syrian man, set himself on fire during the protest. He was hospitalised with burns to his upper body, doctors said.
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About 12,000 refugees remain outside the border village of Idomeni, despite an appeal by the Greek government to move to nearby army-built shelters.
Late on Tuesday, the humanitarian group Doctors of the World, or Medecins du Monde, said it was pulling out of Idomeni because of concerns for its staff amid rising tensions at the camp.
"We left because we felt threatened," group official Antonis Rigas said.
Greek state TV began running short bulletins in Arabic for refugees, urging them to leave the border camp.
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