A woman sits between tents at the port of Piraeus, near Athens, on Saturday, April 2, 2016. (AP)
Several dozen Syrians are also expected to arrive Monday in France, Finland and Portugal, according to German government sources.
The deal has faced strong opposition from rights groups.
Amnesty International has accused Turkey of illegally forcing groups of some 100 Syrians to return every day, saying the alleged expulsions showed "fatal flaws" in the migrant deal agreed with the EU.
Turkey rejects the charge, insisting it still adopts the open-door policy that for the last few years has allowed any Syrian fleeing civil war back home to seek refuge.
There are over 52,000 refugees and migrants currently in Greece, according to official figures.
With most facilities already full, authorities are trying to create space for an additional 30,000 people in new camps.
Adding to the urgency, sporadic violence has broken out between ethnic migrant groups in the overcrowded camps.
But many migrants are reluctant to move to organised centres, fearing that they will not be allowed to leave.
German Interior Minister Thomas de Maiziere, quoted by the Tagesspiegel am Sonntag weekly, voiced optimism on Sunday that the refugee influx had peaked.
But, he suggested, agreements with countries in North Africa may be needed to prevent mass arrivals in future.