Turkish Prime Minister Ahmet Davutoglu said the EU-Turkey deal would likely unravel if Brussels did not relax its visa regime by June.

"This is a mutual commitment. If the EU cannot take the necessary steps required of it, then of course it cannot be expected of Turkey to take these steps," Davutoglu told reporters at Ankara airport before heading to Strasbourg.

Foreign Minister Mevlut Cavusoglu recently told lawmakers in Ankara that Turkey would cancel the agreement if the EU did not keep its word.

"The deal we struck with the EU is very clear. We want this human tragedy to end, our citizens to travel visa-free, and the customs union to be updated," he said in a speech to the parliament. "If the EU doesn't keep its word, including the migrants deal, we will cancel all agreements."

President Recep Tayyip Erdogan - known for his bellicose style - had already warned the EU that there were "precise conditions" in the agreement. But the prime minister's remarks represent the most explicit warning by Ankara to date.

6 billion-euro deal

The deal inked last month aims to discourage migrants from using land and water routes to Greece and Bulgaria by allowing Europe to forcibly return migrants to Turkey.

The deal has been criticized by rights groups for flouting international asylum law and for cozying up to Turkey, where the human rights situation has been declining steadily.

Nevertheless, European leaders have agreed to Turkey's demand of 6 billion euros ($6.7 billion) in payments and political and diplomatic concessions - including visa-free travel for its 75 million citizens.

Davutoglu acknowledged that there are technical requirements Turkey needs to complete before visa-free travel can be implemented. Seventeen of these 75 requirements have yet to be completed, but he said he expected they would be completed by next month.

"Turkey is a serious interlocutor. It does what is has promised and will allow no concessions on what it has been promised," Davutoglu said.

The prospect of visa-free travel for Turkish citizens has been controversial in some EU capitals. The bloc's officials have been accused of bending over backwards to placate Ankara's demands.

German Chancellor Angela Merkel has invested considerable political capital in crafting closer EU-Turkey cooperation over the migrant crisis. Merkel and European Council President Donald Tusk are scheduled to travel to the southern Turkish city of Gaziantep on April 23 to discuss progress on the migrant deal with Turkish leaders.