Greek Prime Minister Kyriakos Mitsotakis on Friday called on Turkey to "take responsibility" for a renewed wave of migrants to Greece, and for an EU-Turkish deal to be revised so Athens can speed up the return of rejected asylum-seekers.

"Turkey must take responsibility" and "control the migrant flow in the Aegean Sea," the conservative Greek leader said during a debate in parliament on migration.

The prime minister indicated that a "stricter" and "more just" amendment to Greece's asylum laws would be put to parliament later this month.

The country has felt under increasing pressure. For the first time since 2016, the country has become the main port of entry into the European Union for migrants and refugees arriving via Turkish shores.

The UN refugee agency (UNHCR) announced on Tuesday that arrivals by sea from Turkey to Greece, mostly Afghan and Syrian families, increased to 10,258 in September.

It said this was the highest monthly total since 2016, when the European Union reached an accord with Turkey to stem the flow of arrivals.

Turkey has welcomed nearly 3.6 million refugees, the vast majority from neighbouring war-ravaged Syria.

Turkish President Recep Tayyip Erdogan threatened in early September to allow a new wave of migrants to go to the EU if he did not receive more international aid.

Ankara wants to create in Syria a "security zone" so migrants can return there. But after a deadly fire at an overcrowded refugee camp on the Greek island of Lesbos on September 29, Athens vowed to return 10,000 migrants who fail asylum requirements to Turkey by the end of 2020.

In four-and-a-half years under the previous left-wing government, Turkey took back fewer than 2,000 people.

"It's crucial that we stick to the letter of the (agreement)," Greek Protection Minister Michalis Chrysohoidis told a news conference in Athens, stressing that the rules must be applied "without nationality restrictions".

EU immigration commissioner Dimitris Avramopoulos said the 2016 agreement "will be enforced".

Avramopoulos was in Athens Friday with German Interior Minister Horst Seehofer to discuss the migrant problem.

"Greece will not be alone," he said, adding that a common European asylum policy is required.

Seehofer said that migrants arriving at European borders requesting asylum "must be shared out in a more logical way. If we do not help Greece, (and other) EU border countries, we will have an irregular migration policy that will lead to deadlock".

Revisions to the EU-Turkey deal to accelerate returns will be discussed at the EU summit later this month. Mitsotakis insists that most new arrivals to Greece are "economic migrants" from Afghanistan or sub-Saharan Africa rather than refugees from Syria.

Copyright Agence France-Presse, 2019