(Adds Davutoglu comments)

By Gulsen Solaker

ANKARA, April 18 (Reuters) - Turkey would no longer need to honor an agreement on migrants with the European Union if the bloc fails to uphold its promise to provide visa-free travel for Turks by June, Turkish Prime Minister Ahmet Davutoglu said on Monday.

Turkey and the EU last month sealed a controversial deal intended to halt illegal migration to Europe in return for financial and political rewards for Ankara.

The EU will take in thousands of Syrian refugees directly from Turkey and reward it with money, visa-free travel and progress in its EU membership negotiations.

"These pledges are mutual. If the EU does not take the necessary steps, it would be unthinkable for Turkey to do so," Davutoglu told a news conference before departing for Strasbourg.

But he said Turkey has been working to fulfill its pledges to the EU and he had no reason to expect a U-turn on the agreement.

"I don't see much of a possibility of EU taking a step to reverse this process after we have come this far," he said.

The EU-Turkey deal aims to discourage migrants from perilous crossings, often in small boats and dinghies, and to break the trafficking rings which have fueled Europe's biggest influx since World War Two.

Seventeen of the 75 requirements required for visa-free travel for Turks by June were yet to be completed, Davutoglu said, adding that he expected those to be fulfilled by May.

"I believe the visa exemption will come into effect in June. If this doesn't happen, obviously nobody can expect Turkey to hold its side of the deal," he added.

Earlier, Foreign Minister Mevlut Cavusoglu said Turkey would cancel its agreements with the EU if the bloc did not keep its word on the deal.

"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."

(Writing by Humeyra Pamuk; Editing by Angus MacSwan)

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