At least 34 people, including 15 babies and children, died after drowning on Sunday when their rickety boat capsized in high winds off a Greek island on Sunday.

The deaths of migrants came at a time when Greek government was angrily defending its handling of the mounting refugee crisis in Europe and sought more help.

Four babies and 11 young children were on the wooden boat when it sank off the island of Farmakonisi. The coastguard frogmen later found eight of the victims in the hold of the boat.

A total of 34 people died, while the coastguard managed to pluck alive 68 migrants from the sea and 30 managed to swim to safety on a beach on the island.

The coastguard claimed the boat was overcrowded and went down because of high winds in the area.

The bodies were taken to Rhodes by a Greek navy ship while the survivors were being transported to Leros. The coastguard was also still searching on Sunday for four children missing after another boat capsized on Saturday off Samos, a Greek island just off the Turkish coast.

Meanwhile, Greece's interim Prime Minister Vassiliki Thanou on Sunday said the criticism of Athens over handling of the crisis is completely "unacceptable".

"Greece is strictly applying European and international treaties without ignoring the humanity of the situation," she said on a visit to Lesbos, an island which has been struggling with the massive influx.

German Chancellor Angela Merkel on Saturday demanded that Athens must make more effort to protect the EU's external borders. "We have a second external border, that's between Greece and Turkey, where we need protection. And this protection is at the moment not being guaranteed. Greece needs to take its responsibility... we will also speak with Turkey," she said.