The warning issued today came as nearly a third of the 52,000 migrants stranded in Greece by European border closures are refusing to move to organized shelters and remain camped out at the port of Piraeus and at the northern border with Macedonia.
More than 4,000 migrants remain at Piraeus, an important site for Greece's vital tourism industry.
"Every effort will be exhausted to persuade refugees and immigrants that it is in their own interest for them to move," a statement from the Greek coast guard said.
Some 4,000 migrants and refugees who reached the Greek islands from Turkey after that date are in detention, with most due to be sent back to Turkish ports. The deportations started Monday and are expected to resume tomorrow.
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More than a million refugees and migrants reached the EU last year, most traveling through Greece and across the Balkans to central Europe.
At Piraeus today, Interior Ministry officials and translators spent hours trying to persuade migrants to move to a new camp in northern Greece, showing them aerial photographs of the site and explaining what facilities are available.
Iranian migrant Ahmad Devidjan said he wasn't sure whether he should move.
"I've been in Greece for 19 days. I went two times to the border with Macedonia, but it was closed. Now I'm back here," Devidjan said. "I have a brother in Germany. He's a teacher. I want to go there.