This migrant death toll is one of the highest since the mass migrant exodus from Turkey to Greece began three years ago.
Sunday is the second anniversary of a European Union-Turkey deal blocking mass migration into Europe.
The incident took place Saturday morning on a highway near the northern city of Xanthi. There still has been no solution on the Greek side, with migrants and refugees still penned up in island holding camps that are often the scene of clashes among migrant groups.
Two women and a man who managed to swim to safety on the island sounded the alarm and several vessels and a helicopter joined in the search for bodies and the missing.
Another three people are missing after the boat went down overnight off the island of Agathonissi as it was carrying migrants from Turkey to Greece, police said.
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If the Security Council is unable to adopt the resolution, then the U.S.is ready to take matters into their own hands. Ambassador Vassily Nebenzia told Reuters .
A coast guard spokeswoman said the recovered bodies had not been identified yet and they included six children.
But hundreds of people, mostly Syrians, Afghans and Iraqis, continue to land every month on the Greek islands that lie just a stone's throw away from the Turkish coast.
The fatalities include five children and 10 adults, a spokesman for the Greek Coast Guard told Anadolu Agency.
Vistas said that while all efforts were now focused on the search and rescue operation, "it is clear that the solution is in (providing) measures for the protection of people" and in providing safe procedures for refugees and migrants while also cracking down on smuggling rings.
A massive search operation involving aircraft, the Greek navy and coast guard and a vessel from the European border agency Frontex was underway.
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