“We will continue to implement it out of humanitarian reasons,” he added.

He said that the one-to-one mechanism, by which the EU resettles a Syrian refugee from Turkey for every migrant that Turkey takes back from Greece, was working.

But he warned that Turkey would not be ready to do more as long as there is no easing of the visa regime for its citizens traveling to Europe.

"Without visa liberalisation, Turkey will not be part of any new mechanism," he said.

The acceleration of the visa liberalisation process was promised by the EU as part of the March deal, under the condition that Turkey fulfills 72 benchmarks.

Six of them remains to be met, including a change in Turkey's anti-terror law, which the EU says uses defines terrorism too broadly.

Celik warned that Turkey would not amend the law as long as Turkey faces a terrorist threat.

"It is not rational to expect from Turkey to make any change in Turkish anti-terror law" in current circumstances, Celik said, referring to the recent wave of attacks in Turkey attributed to the Islamic State and the Kurdish PKK guerillas.

Ankara's position on anti-terror law and visa liberalisation leaves the EU in a dilemma over whether to accept a watering down of its requirements to maintain Turkey's cooperation in the migration crisis.

Whereas EU diplomacy chief Federica Mogherini said that management of the migration crisis and visa liberalisation were "separate issue[s]", Turkey has lumped both together and has ruled out agreement to EU demands for change.

Instead Celik said that Turkey could take "some commitments about some steps" that would reassure the EU and the Council of Europe that it would not use its legislation extensively in a way that threatens the rule of law.

"In the meantime we could go ahead with visa liberalisation," he said.

"Work is ongoing," Mogherini said, adding that she hoped that the EU would "manage to end in the direction that politically we decided".

'First class democracy'

The priority for the EU on Saturday was to renew a dialogue with Turkey after weeks of criticism by Turkish officials of the EU's lack of solidarity in addressing the attempted coup in July, reciprocated by the EU criticism of Ankara about the crackdown that followed.

The meeting between EU ministers and Turkey's Celik was "long and very substantial," an EU source said. "It was very fruitful," Celik told journalists.

He said that he "expressed clearly" to EU ministers that his government and the Turkish people "were disappointed" by the EU's lack of support after the failed coup.

"Turkey has a first class democracy," he said. "No one should be teaching democracy lessons to Turkey. Turkey has democracy lessons to teach to others."

EU ministers, for their part, reiterated their support of Turkey's democratic institutions and, according to Celik, "with very good will said they understood that solidarity they expressed was not sufficient".

EU officials felt that some kind of mea culpa was necessary to resume dialogue with the Turks because "their pride was injured," the EU source said.

Several ministers and officials recognised that the EU had underestimated the shock the coup was for Turkish officials.

"Some of them were directly targeted, they were supposed to be killed," the source noted.

In a statement that was used both by Mogherini and Celik, the EU and Turkey agreed that they need to "talk less about each other and more with each other".

After Austria's push for a suspension, doubts about the future of EU accession negotiations with Turkey were also apparently erased.

Mogherini insisted that Turkey was still an EU candidate country, which gave the EU the right to have dialogue with "no taboo" on issues such as the rule of law, the right to fair trial or freedom and expression and the media.

The main issue that could block the process could be the re-introduction of the death penalty in Turkey. But Celik assured the EU that the death penalty was not on the Turkish assembly agenda and that "no decision whatsoever" as been taken about it.