IZMIR: Turkey and Greece vowed close cooperation on Tuesday on a plan to send back migrants rejected by Europe, laying aside historic differences in an agreement they hope will end illegal flows of people across the Aegean Sea.

Greek Prime Minister Alexis Tsipras told a joint news conference with his Turkish counterpart Ahmet Davutoglu that the readmission agreement would help to reduce the "unbearable flow" into Europe.

"(It) sends a clear message to migrants coming from third countries, rather than countries at war, ... that there is neither the political will (to allow their passage) nor the ability to cross to Europe," he said after meetings in Turkey's Aegean coastal city of Izmir.

"This is the reality we ought to sincerely convey to them in order to stop, to reduce, this unbearable flow for our countries."

The prime ministers were meeting a day after Ankara offered to the EU to take back all migrants who cross into Europe from Turkish soil in return for agreement in principle on its demands for more money, faster EU membership talks and earlier visa-free travel.

More than a million people fleeing war and poverty in the Middle East and beyond have flooded into the EU since early 2015, most making the perilous sea crossing from Turkey to Greece, then heading north through the Balkans to Germany.

A Greek official said that while Turkey and Greece had had a readmission agreement for some time, the deal signed on Tuesday changed the mechanism so that illegal migrants could be sent back immediately.

"The aim here is to discourage irregular migration and ... to recognise those Syrians in our camps who the EU will accept - though we will not force any one to go against their will - on legal routes," Davutoglu said, adding that there would be no extra financial burden on Turkey.

"Europe will cover all costs of readmitting migrants from the Aegean, the readmission costs (including) returning to Turkey and to a third country, or their own country," he said.

"IMPORTANT VICTORY"

Davutoglu heralded what he described as an "important victory for our citizens" in the agreement from EU leaders to bring forward visa liberalisation for Turks to June from the end of 2016. He vowed Turkey would pass the necessary legislation in the coming months to see it implemented.

The EU agreed to the earlier target date provided Ankara meets all the conditions including changing its visa policy towards Islamic states and introducing harder-to-fake biometric passports.

"We will pass the legislation needed for visa-free (travel) in the coming months," he said, and called on Turkey's opposition parties to support the effort in parliament.

Tsipras said the two countries would step up efforts to tackle people smugglers in the Aegean Sea and would not simply implement "some plan imposed on us by some of our partners".

The EU leaders pledged on Monday to help Greece cope with a backlog of migrants stranded on its soil and welcomed NATO naval back-up in the Aegean.

NATO Secretary-General Jens Stoltenberg said on Monday the alliance had begun patrols to support efforts to locate migrant boats, overcoming territorial sensitivities in Greece and Turkey to patrol in the waters of both NATO states.

"Putting aside our differences on the Aegean (territorial dispute), both Turkey and Greece have displayed a mature attitude in relation to the operations NATO will undertake," Davutoglu said. "We may have differences in perspective but this is not an obstacle to cooperation."

Davutoglu also said a resolution of the division of Cyprus was close. The island has been split along ethnic lines since 1974. The EU considers the Greek Cypriot government in Nicosia to represent the whole island, while Ankara recognises a breakaway Turkish Cypriot administration in the north.