At least 13 people, including six children and a baby, have died after a boat carrying refugees set for Greece came into difficulty, the Greek coastguard said on Wednesday, according to various media outlets.

"Fifteen people were able to be saved from the sea. One refugee is still missing," a coastguard officer reportedly said.

The accident occurred off the small Aegean island of Farmakonisi.

Two of those saved remain in a critical hypothermic condition and have been taken to a hospital on nearby Kos for medical treatment, state radio reported.

Fishermen and the coastguard carried out a rescue mission on Wednesday morning, according to the report. A helicopter was also deployed to search the area for survivors.

The Geneva-based International Organization for Migrants says more than 1 million people have entered Europe as of Monday. Almost all came by sea, while 3,692 drowned in the attempt.

At least 820,000 refugees and economic migrants have reached Greece's eastern islands this year. Nearly all have continued north, hoping for a better life in wealthier European countries.