Turkish President Recep Tayyip Erdogan has warned the European Union that his country's parliament would block laws related to a deal to stem the flow of migrants to Europe, if Ankara was not granted its key demand of visa-free travel.

This includes readmitting migrants who crossed illegally. The stark and unexpected warning from Erdogan came amid spiralling tensions between the Turkish president and the bloc.

"Right now, on June 1st there was to be a step toward the readmission agreement. And on June 30 a step was to be taken in terms of the visas," said Erdogan.

"Our friends will be talking on the subject, our foreign minister, European Union ministers will hold meetings. And at these talks, results will either be obtained or not."

"And if they aren't, I'm sorry, a decision, a law toward the readmission agreement, toward its implementation, will not pass in the parliament of the Republic of Turkey."

EU leaders are insisting that Turkey abides by 72 conditions before the visa exemption takes place -- a demand to change Turkey's counter-terrorism laws is proving particularly contentious.

There have been growing indications Turks will not be given the visa-free travel by the end of June. And German Chancellor Angela Merkel warned after talks with Erdogan on Monday that the target was unlikely to be met.

The agreement saw Turkey stop migrants from crossing the Aegean to Europe and also readmit migrants who crossed illegally.

EU officials have hailed the success of the deal, but Ankara has grown increasingly uneasy about the bloc's wariness in holding up its end of granting visa exemption and billions of euros.