Ten people, including a child, drowned when a boat carrying about 100 migrants capsized off Greece on Sunday, as Athens angrily defended its handling of the swelling refugee crisis.

Interim Prime Minister Vassiliki Thanou branded criticism of Greece, which has been on the frontline of the surge of migrants trying to reach Europe, as "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.

The coastguard said the 10 people drowned when their stricken boat went down off the island of Farmakonisi in the southern Aegean Sea, while another 68 people were rescued.

A further 29 managed to swim to a beach on the island, but the coastguard recovered the bodies of 10 people, including a child.

The coastguard was also still searching for four children missing after another boat capsized on Saturday off Samos, a Greek island just off the Turkish coast.

The latest tragedies follow the death of a Syrian toddler whose lifeless body was photographed washed up on a Turkish beach, becoming a heartwrenching symbol of the plight of refugees fleeing war.

The International Organisation for Migration has said over 430,000 migrants and refugees had crossed the Mediterranean to Europe so far in 2015, with 2,748 dying or going missing en route.

German Chancellor Angela Merkel on Saturday called on Athens, while facing its own deep economic crisis, to 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," she said.

"Greece needs to take its responsibility... we will also speak with Turkey."