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Greece's new minister for migration said Monday he would consider it "unthinkable" for the European Union to pull out its border protection force from the country, and promised to address a growing list of international grievances over dealing with migrants.

A dispute between Greece's government and the EU border agency Frontex worsened after a trawler carrying hundreds of migrants sank off the coast of the Greek mainland on June 14, leaving more than 500 people feared dead.

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Frontex has also given Greece until July 10 to provide explanations regarding new reports of alleged illegal deportations – known as pushbacks – of migrants on the Greek island of Lesbos.

Dimitris Kairidis

Greek Migration and Asylum Minister Dimitris Kairidis on Monday sharply rebuked European border security agency Frontex's criticisms of the nation's handling of migrant deaths of its coast, calling the agency's threats of withdrawal "unthinkable." (AP Photo/Petros Giannakouris)

Dimitris Kairidis, the migration minister, said he would meet with Frontex officials in Athens and at the agency's headquarters in Warsaw, Poland in the coming days.

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"I think it would be unthinkable for Frontex to leave our country," Kairidis told state-run ERT television. "They would be shooting themselves in the foot. Their main purpose is to the protect the borders of the European Union."

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Kairidis was sworn in as minister last week following the re-election victory of Greece's conservatives. He confirmed Monday that consultations with Frontex had already taken place "regarding its presence in Greece – nothing more."