With Ankara close to finalizing all the necessary work before May 4 for Turkish nationals to be granted visa-free travel to the European Union's Schengen zone, EU High Representative for Foreign Affairs and Security Policy Federica Mogherini said Tuesday that Turkey will be granted visa liberalization once all benchmarks have been fulfilled.Ankara has demanded its citizens be allowed to enter the EU's passport-free Schengen zone without visas by June in exchange for it taking back migrants who traveled to Europe from Turkey. Turkey must meet 72 criteria before being granted visa-free travel."On free travel, this will be done only once all the criteria are respected, as for all countries with which we negotiate free travel for a limited period," Mogherini said on France Inter radio.In spite of doubts from some EU official that Turkey would be able to meet all benchmarks before May 4, the day the European Commission will share its views on granting visa-free travel to Turkish citizens, Daily Sabah learned last week that the government was working around the clock to pass the necessary legislation and that all 72 benchmarks will be met at the end of this week at the latest."We will have fulfilled all requirements that the European Union put forward for visa liberalization. As a matter of fact, Parliament's schedule has been adjusted accordingly regarding this issue," Parliament Foreign Affairs Commission member and Justice and Development Party (AK Party) Samsun Deputy Hasan Basri Kurt told Daily Sabah.Kurt said last week that Parliament's schedule was greatly adjusted for this task. "Everything will be wrapped up next week [this week] if nothing extraordinary comes to the agenda in Parliament. It is not possible that the European Commission report will suggest anything negative concerning lifting visa requirements for Turkish citizens," he said.The EU struck a deal with Ankara to send back to Turkey all irregular migrants who arrive in Greece after March 20 in a bid to halt the mass migration that has created enormous strain in Europe. The deal also promises to speed up talks on Turkey's EU accession process.Two sets of deportations of 325 migrants from Greece took place three weeks ago and another 49 were sent back Tuesday.The deal has already sharply reduced the number of people crossing from Turkey to Greece. Greek Prime Minister Alexis Tsipras as well as a European Commission report said the implementation of last month's EU-Turkey agreement to curb migration had allowed for progress. Migrant flows to Greece decreased markedly in recent months, Tsipras said on Wednesday, defending his government's support for the deal."A few months ago we had flows of 3,000 to 4,000 daily to our islands. ... Today, the flows are about 50 to 60 daily," Tsipras told Greek parliament during a debate on security.Visa liberalization a must to continue migrant dealAs Ankara awaits the European Commission report on May 4, President Recep Tayyip Erdoğan and Prime Minister Ahmet Davutoğlu have continuously warned the 28-nation bloc that Turkey would end the migrant deal if visa liberalization were not granted.Davutoğlu said on Tuesday that the deal could be implemented together with visa liberalization. "We are waiting for the European Union to do what falls on its shoulders and complete the judicial process without putting forward any political excuses regarding visa liberalization," he said, adding that if it does Turkey will not keep its side of the bargain.Erdoğan also warned EU. "Turkey will not implement the Turkey-EU deal on stemming the illegal flow of migrants to Europe unless the 28-nation bloc fulfills its side of the agreement," he said in a speech at the Presidential Palace on April 7."Everything that has been promised [must be put into action by the EU]; everything specified under the accord. "There are precise conditions. If the European Union does not take the necessary steps, then Turkey will not implement the agreement," Erdoğan said.