Last month 3,360 migrants and refugees landed on the Greek islands, compared with 26,971 in March -- an 88 per cent drop, according to figures from the International Organization for Migration (IOM).
The EU border agency Frontex also reported what it described as a "dramatic" slowdown, saying it had registered 2,700 arrivals in Greece last month.
The figures are the first for a full month-long period since the EU-Turkey deal came into force in March and will be seen as a key measure of its effectiveness.
Under the March deal, Turkey agreed to take back Syrian migrants landing on Greek islands in exchange for incentives, including billions of euros in aid and visa-free European travel for its citizens.
The agreement is the cornerstone of the EU's plan to curb a crisis that has seen 1.25 million Syrian, Iraqi, Afghan and other migrants enter Europe since January 2015.
With Turkey's military battling rebels from the Kurdistan Workers' Party (PKK) in the Kurdish-majority southeast, Ankara has said that it cannot change its anti-terror legislation.
Ankara must also fulfil four other outstanding conditions including anti-corruption and data protection issues. Turkey has so far complied with 67 requirements of the deal.
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