"Europe...Must share out responsibility among all member states," Tsipras said after his oath of office.
"Otherwise there is no point in talking about a united Europe..If everyone looks to one's own yard when we have a common home, things will be ominous," he said.
EU interior ministers will meet tomorrow to try to coordinate their response to the crisis ahead of an emergency summit set to open on Wednesday.
Over 310,000 migrants and refugees have landed on Greek shores from Turkey this year, most of them Syrians fleeing their country's civil war.
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In Hungary, police have used water cannons to push back refugees and border-crossing has been made a crime punishable by up to five years in jail.
Greece itself has been criticised for making little preparation to deal with the human wave during the summer, leaving entire families sleeping in the open with little access to medical care and sanitation.
But Tsipras said today that "Europe until now had not taken care to protect countries of first arrival from a wave that is taking unchecked proportions.