Greece's prime minister said on Friday he was ashamed to be a member of a European Union that he said was sidestepping responsibilities over the migrant crisis and crying hypocritical tears for children who have drowned trying to reach its shores.

In some of the hardest-hitting comments yet on a crisis resonating throughout Europe, Alexis Tsipras told parliament Greece didn't want a "single euro" for saving lives as thousands of refugees continued to arrive daily on its shores, and the EU remained at odds on how to deal with the influx.

At least 35 people drowned trying to cross the sea between Turkey and Greece this week. Authorities fear the death toll will rise as more people attempt the short but dangerous passage to Greece before the onset of winter.

"I feel ashamed as a member of this European leadership, both for the inability of Europe in dealing with this human drama, and for the level of debate at a senior level, where one is passing the buck to the other," Tsipras told parliament.

Impoverished Greece has been a transit point for more than 570,000 refugees and migrants fleeing conflict in the Middle East and beyond since January, triggering bickering among European nations.

Speaking during prime ministers' question time, Tsipras also said any suggestion that Greece was not effectively safeguarding the EU's outermost borders – he referred to leaders of "certain European countries" – was born out of ignorance of international law dictating protection of the lives of people in distress at sea.

"These are hypocritical, crocodile tears which are being shed for the dead children on the shores of the Aegean. Dead children always incite sorrow. But what about the children that are alive who come in thousands and are stacked on the streets? Nobody likes them."

EU states 'wagging finger'

The humanitarian crisis is adding to misery in Greece, which was forced to seek a third international bailout this year to stave off bankruptcy and its exit from the euro.

Tsipras said it was important that the European Union had begun a dialogue with Turkey on the creation of so-called hot spots to register refugees on Turkish soil and for effective patrols along Turkey's shoreline.

But he said there should be more effective focus on patrolling Turkey's sea border to ensure that refugees did not risk their lives getting to Europe in the first place.

Greece has agreed to temporarily host up to 50,000 refugees pending their relocation to other countries. That agreement was struck at a meeting of several European nations last Sunday in Brussels.

Although his migration minister was quoted as saying earlier this week that EU financing was needed for a subsidised housing programme to work, Tsipras said Greece did not expect to get paid for saving lives.

Over just a two-day period on October 29 and 30, 595 refugees were rescued at sea, the coastguard said.

"Greece is in crisis. We are a poor people, but we have retained our values and humanity, and we aren't claiming a single euro to do our duty to people who are dying in our back yard," Tsipras said, after an opposition lawmaker asked what Greece had received in return for agreeing to host refugees.

His country, he said, couldn't put a price on the human cost. "I'm not addressing you," he told a lawmaker. "I'm addressing those European partners who are wagging their fingers at Greece."