Boats smuggling migrants sank off the coast of two Greek islands, Kalolimnos and Farmakonissi
The Greek coast guard says at least 40 people died when boats smuggling migrants capsized in two separate incidents.
A search and rescue operation is under way after the two wooden boats sank.
One went down off the coast of the island of Kalolimnos, and the coast guard said it has recovered the bodies of 16 women, 11 children and seven men. Around 25 have been rescued.
Earlier six children and one man drowned when another boat sank off the island of Farmakonissi to the north.
Meanwhile the Turkish coast guard has found the bodies of three children after their boat sank off the beach resort of Didim.
Thousands of people fleeing war and poverty in the Middle East - many of them Syrian refugees - continue to arrive from Turkey in flimsy boats every day.
The International Organisation for Migration (IOM) estimates that some 31,000 migrants have reached Greece by sea so far this year, hoping to start new lives in Europe.
On Thursday at least 12 migrants, including children, drowned off the Turkish coast as their boat tried to reach Greece. The Turkish coast guard rescued 28 people.
The Irish Government is being urged to send another naval vessel to deal with the migrant crisis following the latest fatalities.
Ireland has already sent three vessels to the Mediterranean - but the last naval crew returned home before Christmas.
CEO of the Immigrant Council of Ireland, Brian Killoran, says we are still needed, and says that "while the naval presence in the Mediterranean was suspended, the movement of people didn't actually stop this winter, which was highly unusual".
German Chancellor Angela Merkel said she will press Turkey to step up to its "key role" in stemming the flow of migrants to Europe, when she hosts Prime Minister Ahmet Davutoglu for talks on Friday.
Meanwhile, the migrant and refugee crisis is also being keenly discussed at the World Economic Forum in Davos where world leaders have been gathering amid fears that the EU's freedom of movement principle is at risk.
The Dutch and Swedish prime ministers told WEF audiences that Europe has just six to eight weeks to save the 26-nation Schengen zone of passport-free travel from collapse.
Austria has announced more border controls this week and German President Joachim Gauck told the Davos audience there would be nothing immoral about putting a limit on the number of asylum-seekers a country could absorb.
It comes after more than a million migrants and refugees crossed into Europe in 2015, according to the International Organisation for Migration (IOM).
French Prime Minister Manuel Valls has warned that Europe's migration crisis is putting the European Union (EU) at grave risk.
Speaking during an interview with BBC News, Mr Valls has said that Europe could not take all the refugees fleeing what he called 'terrible wars' in Iraq or Syria.
He added that, "it's Europe that can die, not the Schengen area, if Europe is not capable of protecting its own borders. It's the very idea of Europe that will be questioned"
You can watch Mr Valls' interview with BBC here.