More than 70 people survived, and a large air and sea search-and-rescue effort was underway off the eastern islet of Kalolimnos, the site of the worst accident. It was not clear how many people were on board the wooden sailboat that sank there in deep water, leaving at least 35 dead.
At least 800 people have died or vanished in the Aegean Sea since the start of 2015, as more than a million refugees and economic migrants entered Europe. About 85 per cent crossed to the Greek islands from Turkey, paying large sums to smuggling gangs with unseaworthy boats.
Rights groups said the deaths highlighted the need for Europe to provide those desperate to reach the prosperous continent with a better alternative to smuggling boats.
"These deaths highlight both the heartlessness and the futility of the growing chorus demanding greater restrictions on refugee access to Europe," said John Dalhuisen, Amnesty International's Europe and Central Asia programme director.
"A manageable crisis has become a moral test that Europe is in danger of failing dismally."
The UN refugee agency said daily arrivals on the Greek islands had surged to more than 3000 in the past two days, and it cited refugee testimony that smugglers had recently halved their rates amid deteriorating weather.
German Chancellor Angela Merkel met Turkish Prime Minister Ahmet Davutoglu in Berlin and they pledged to work intensively together not only to stem the flow of people but to improve conditions in camps in Turkey and to try to bring about a peace deal in Syria.
"The refugee crisis is not Germany's crisis, it is not Europe's crisis, it is not Turkey's crisis," Davutoglu said in a joint news conference. "It is a crisis that was born out of the crisis in Syria. If we co-operate, we can bring this crisis under control. If we throw the issue at each other, solving this issue will become more difficult."
Germany had an unprecedented 1.1 million asylum-seekers arrive last year, many of them fleeing conflicts in Syria, Iraq and Afghanistan.
Turkey hosts more than 2.2 million Syrian refugees from a nearly five-year civil war that has killed a quarter of a million people and displaced half the country. Peace talks are scheduled to begin today in Geneva, although officials say they may be delayed by a few days.
European Union foreign policy chief Federica Mogherini warned that the 28-nation bloc faced big economic risks if its members started erecting barriers to borderless travel.
In the first sinking before dawn in the eastern Aegean, a wooden boat carrying 49 people went down off Farmakonissi islet. Forty people made it to shore. A few hours later, a sailboat sank off Kalolimnos, south of Farmakonissi. The coast guard rescued 22 men and four women, and recovered 35 bodies: 17 women, seven men and 11 children.