One of the boats had around 100 migrants aboard when it sank north of the Greek island of Lesbos, it said.
The new accidents brought to 34 the number of migrants found dead in Greek waters this month, according to an AFP tally based on data from Greek port police.
Since the start of the year, 560,000 migrants and refugees have arrived in Greece by sea, out of over 700,000 who have reached Europe via the Mediterranean, according to the International Office for Migration (IOM).
Also today, Europe's Operation Sophia rescued about 1,000 migrants from six dinghies and a fishing boat off the Libyan coast, the Italian coastguard said.