Migrants sent back from the Greek island of Lesbos began arriving in Turkey on Monday under a European Union deal aimed at stopping the influx of migrants and refugees into Europe since last year.

The first of two Turkish-flagged passenger boats carrying 131 migrants arrived in the Turkish town of Dikili early on Monday, accompanied by two Turkish coast guard vessels and a police helicopter buzzing overhead, a Reuters witness said.

Under the EU-Turkey deal, Ankara will take back all migrants and refugees who enter Greece illegally, including Syrians, in return for the EU taking in thousands of Syrian refugees directly from Turkey and rewarding it with more money, early visa-free travel and progress in its EU membership negotiations.

A few dozen police and immigration officials waited outside a small white tent on the quayside as the migrants began to disembark behind security fencing.

There were no Syrians in the first group of migrants coming to Turkey from Greece, Turkish EU Affairs Minister Volkan Bozkir said.

He said Syrian migrants coming from Greece will be sent to the southern Turkish city of Osmaniye. Bozkir also said that Syrians taken from camps in Turkey will be sent to Germany, from where they will be sent on to other countries.

The returnees were primarily from Pakistan and some from Bangladesh and they had not applied for asylum, said Ewa Moncure, a spokeswoman for EU border agency Frontex.

Asked if Syrians would be returned, she said: "At some point, but I don't know when."

On Lesbos, a small group of protesters outside the port chanted "Shame on you!" when the migrant boats set sail as the sun rose over the Aegean Sea. Volunteer rescuers aboard a nearby boat hoisted a banner that read: "Ferries for safe passage, not for deportation."

Each migrant was accompanied on Lesbos by a plainclothes Frontex officer. They had been transported in a nighttime operation from the island's holding centre to the port. Greek riot police squads also boarded the boats.

Moncure said there were plans to return migrants from the nearby island of Chios as well but did not say when.

The UN High Commissioner for Refugees (UNHCR) and rights groups have said the deal between the European Union and Turkey lacks legal safeguards.

Amnesty International has called it "a historic blow to human rights", and was sending monitors to Lesbos and Chios on Monday.

More than 3,300 migrants and refugees are on Lesbos. About 2,600 people are held at the Moria centre, a sprawling complex of prefabricated containers, 600 more than its stated capacity. Of those, 2,000 have made asylum claims, UNHCR said. - Reuters