Turkey would have to back out of its agreement with the European Union to stem the flow of refugees and migrants into the bloc if the EU does not deliver visa-free travel for Turks, Foreign Minister Mevlut Cavusoglu has said.

Visa-free access to the EU - the main reward for Ankara's collaboration in cutting off an influx of refugees and migrants into Europe - has been subject to delays due to a dispute over far-reaching Turkish legislation and Ankara's crackdown after a failed coup.

Cavusoglu told Germany's daily Frankfurter Allgemeine Zeitung the agreement on stemming the refugee flow had worked because of "very serious measures" taken by Ankara.

"But all that is dependent on the cancellation of the visa requirement for our citizens, which is also an item in the agreement of March 18," Cavusoglu said in a release in advance of comments to be published in the newspaper's Monday edition.

"If visa liberalisation does not follow, we will be forced to back away from the deal on taking back [refugees] and the agreement of March 18," he said, adding that the Turkish government was waiting for a precise date for visa liberalisation.

"It could be the beginning or middle of October - but we are waiting for a firm date."

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The EU-Turkey agreement was designed to halt the flow of refugees and migrants by deporting them back to Turkey from Greece and allowing a number of Syrians to participate in a relocation programme from Turkey to the EU.

The deal was widely criticised by humanitarian groups and rights organisations, many of which claimed it violated international law.

In June, the medical aid charity Doctors Without Borders (MSF) said it will reject all funding from the European Union in protest of the agreement.

MSF received $63m, about 8 percent of its total budget, from European Union institutions and its 28 member states last year.

"The EU deal is the latest in a long line of policies that go against the values and the principles that enable assistance to be provided," Jerome Oberreit, the secretary general of MSF, said at the time.

"We cannot accept funding from the EU or the member states while at the same time treating the victims of their policies. It's that simple."

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European Commissioner Guenther Oettinger said recently he did not see the EU granting Turks visa-free travel this year due to Ankara's crackdown after the failed military coup in mid-July.

Fleeing war and economic devastation, more than a million refugees and migrants arrived in Europe by boat in 2015, according to the United Nations refugee agency (UNHCR). More than 251,000 have made the dangerous journey so far this year.

At least 3,034 refugees perished on the Mediterranean Sea between January 1 and July 28 of 2016, compared with 1,970 in almost the same period a year earlier - an increase of 54 percent, according to the International Organisation for Migration (IOM).