Restrictions have resulted in a build-up of more than 3,000 asylum seekers at the Greek-Macedonian border.
At least 11 people including children have died and 13 others remain missing after a boat carrying about 50 refugees sank in the eastern Aegean Sea, Greek authorities say.
The coast guard said the accident occurred early on Wednesday when a wooden boat carrying the refugees from Turkey sank near the islet of Farmakonisi.
At least 26 people have been rescued alive.
The dead were five children, four men and two women. Their nationalities were not immediately known.
The latest incident happened just a day after six Afghan children drowned off the coast of the western Turkish province of Izmir, as the rubber dinghy they were in sank before reaching the Greek island of Chios.
Greece is the main entry point for refugees seeking a better life in the European Union.
More than 600,000 people have arrived in Greece this year by making the short but perilous journey by boat or rubber dinghy from Turkey to outlying islands. Thousands more have drowned.
The latest drownings came as witnesses said Greek police started removing hundreds of refugees stranded on the Greek-Macedonian border and blocking rail traffic.
About 1,200 people – mostly from Pakistan, Morocco and Iran – were stuck near the northern Greek town of Idomeni, demanding to cross into Macedonia to reach northern Europe after non-EU Balkan states began filtering refugees by nationality.
The police official said the refugees would be taken to Athens on buses and will be accommodated in centres before being sent back to their home countries.
Hundreds of thousands of people streamed into Europe this year, mostly through Greece, but Balkan states began blocking passage last month to all but Syrians, Iraqis and Afghans, who are considered as refugees because they are fleeing war zones.
Clashes have flared in the past two weeks between police and stranded migrants blocking the Greek-Macedonian crossing for refugees and the railway line running between the two countries.
A Moroccan man was electrocuted on the line last week.
Macedonia has erected a metal fence to keep others out and plans to extend it to cover more than 40km of the border.