Greece sent back a first wave of migrants to Turkey on Monday under an EU deal to ease its migration crisis that has run into heavy criticism from rights groups.

At first light, a small Turkish ferry, the Lesvos, and a larger catamaran, the Nezli Jale, steamed out of the island of Lesbos carrying 131 migrants, mainly from Pakistan and Bangladesh, said EU border agency Frontex, which is escorting them to Turkey.

Police and riot officers were present, but "the procedure was very calm, everything was orderly," Frontex spokeswoman Ewa Moncure told reporters at Lesbos harbour.

Another Turkish catamaran carried migrants from the neighbouring island of Chios. Officials have not yet confirmed how many people are on board.

A few dozen activists on Chios gathered near the embarkation site to protest against the deportations, chanting "Freedom," an AFP photographer said.

"Stop the dirty deal", "stop deportations" and "wake up Europe" were among the banners brandished in Lesbos against the disputed EU-Turkey agreement.

A couple of hours later, the first ferry docked in the Turkish coastal town of Dikili, according to AFP reporters at the scene.

Red tents have been set up along the town's harbourside to receive the arrivals.

However, Mustafa Toprak, governor of Turkey's Izmir region, said the migrants would only be staying briefly in Dikili and the resort of Cesme -- a second reception point -- before being moved on.

Turkey and the EU clinched the agreement in March, with the 28-nation bloc desperate to stem its worst migration crisis since World War II.

Under the terms of the deal, all "irregular migrants" arriving since March 20 face being sent back, although the accord calls for each case to be examined individually.

For every Syrian refugee returned, another Syrian refugee will be resettled from Turkey to the EU, with numbers capped at 72,000.

In Monday's first wave, Turkish Interior Minister Efkan Ala has said his country was ready to receive 500 people and that Greek authorities had provided 400 names, although these numbers could change.

Police sources on Lesbos, a Greek holiday island that has served as the gateway for hundreds of thousands of people coming from Turkey, said there had been a flurry of last-minute asylum applications.

"We... have over two thousand people that have stated their wish to seek asylum and we need to see a credible process go ahead with the Greek asylum service for those that wish to express their protection concerns," said Boris Cheshirkov, the UN refugee agency spokesman on Lesbos.

Greek officials have been tight-lipped over how many migrants will cross the Aegean Sea back to Turkey.

State news agency ANA reported that some 250 migrants from Bangladesh, Pakistan, Sri Lanka and African nations would be sent back daily between Monday and Wednesday.

Yiorgos Kyritsis, spokesman for Greece's refugee coordination unit, insisted Monday's operation only "involves people who have not requested asylum".

Rights groups have criticised the deal, questioning whether it is legal and ethical.

"We don't know what is going to actually happen," senior UN migration official Peter Sutherland admitted this weekend.

"But if there is any question of collective deportations without individuals being given the right to claim asylum, that is illegal."

Amnesty International says Turkey is not a safe country for refugees -- a charge Ankara rejects.

Many migrants on the islands have complained of not being given sufficient time and access to carry out the asylum procedure.

Vassilis Balas, manager of the Suda refugee camp in Chios, said many migrants had only just started applying.

"UNHCR (the UN refugee agency) is facilitating this process in the camps. It's facilitating a process that actually should have been done by the police and other authorities in the hotspot," he said.

The operation to resettle Syrians to Europe under the one-for-one arrangement also starts Monday.

Germany expects to take in a first group of about 35 Syrians from Turkey on Monday, the German interior ministry said.

Several dozen others are expected to arrive in France, Finland and Portugal, according to German government sources.

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