"I hope they will keep the promise that they made and close this issue by October at the latest," he added.

The deal agreed in March by EU leaders and Turkish prime minister Ahmet Davutoglu said that visa liberalisation should be granted by the end of June at the latest, if Turkey fulfilled all the required 72 benchmarks.

Last week the EU Commission proposed lifting the visa requirements, even though Turkey fell short on five criteria.

Erdogan's comments came as it emerged that the European Parliament, which will also have to agree to grant visa free travel, would not begin discussing the issue until all the 72 required benchmarks are met by Turkey.

The EP's last plenary session will be in the first week of July before the summer break, making it almost impossible to meet the summer deadline.

In a sign that the Turkish president might have resigned himself to that political reality, he recalled an earlier pledge from EU leaders.

In his speech Erdogan was referring to an earlier EU-Turkey statement from November last year, that stated that if all requirements are met, the visa free travel should be granted by October 2016.

In any case, the 72 benchmarks would still need to be met by Turkey for the visa liberalisation to happen.

One of the crucial outstanding criteria is narrowing the definition of terrorism and terrorist acts in Turkish law, so that it could not be used to prosecute journalists, academics or opposition figures.

Erdogan last week warned he would not change the anti-terror law for the sake of visa-free travel. on Tuesday he sounded equally defiant on that point.

The president, in a reference to tents set up by Kurdish activists near the EU Council building in Brussels in March, asked why "terrorists" were allowed to pitch camp outside the building.

"First give an answer to that" before Turkey examines its anti-terror laws, he said.

The visa liberalisation is a key component of the EU-Turkey deal aimed at stemming the flow of migrants into Europe. The number of arrivals have sharply dropped since the deal kicked in late March.

But Erdogan has threatened before that the deal could unravel if Turkish citizens are not granted visa free access to the Schengen zone.

Concerns over Turkey's commitment to the agreement grew after Davutoglu, an architect of the deal, said last week he would resign as prime minister.