"We do have figures on the arrivals through the Aegean from Turkey into Greece, which show there has been a dramatic and sharp decrease in the number of people crossing the Aegean since the entry into force of the EU-Turkey agreement, and has been sustained for the moment," Bertaud said at a briefing.
In mid-March, the European Union and Ankara agreed on a deal under which Turkey pledged to take back all undocumented migrants who arrive to the European Union through its territory in exchange for Syrian refugees accommodated in Turkey, on a one-for-one basis.
In return, the bloc pledged to provide a total of 3 billion euros ($3.4 billion) to Turkey to help it deal with refugees, with a possible further 3 billion-euro provision in 2018. The 28-member bloc also agreed to accelerate the Turkish EU accession bid and introduce a visa-free regime between Turkey and Europe.
In early April, Turkish Prime Minister Ahmet Davutoglu claimed that the flow of migrants to Greece had reduced "significantly" since the Turkey-EU deal came into effect.