At a tense meeting of European Union interior ministers in Amsterdam, Austria and Germany urged Athens to do more to deal with the continent's biggest crisis of its kind since World War II.
But Greece's interior minister for migration Yiannis Mouzalas insisted his country -- already buffeted by a debt crisis that almost drove it out of the euro last year -- was doing its best in difficult circumstances.
The short sea crossing from Turkey to the Greek islands accounted for most of the one million migrants and refugees who arrived in Europe last year, but Mouzalas said it would be illegal to push back migrants from Greek waters.
"According to international law, to the law of the sea, according to the Geneva Convention, according to the European, to the Greek law, the only way to act on the sea border is to make rescue," he said.
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Last week Austrian Interior Minister Johanna Mikl-Leitner warned Athens could face "temporary exclusion" from Schengen, the 26-country zone of mainly EU countries that embodies the European dream of free movement.
Austria, Germany and several other Schengen member states have already reintroduced temporary checks at their internal borders, raising fears the passport-free system could collapse.
"Greece has to reinforce its (border) resources and accept help," Mikl-Leitner told reporters in Amsterdam today, adding that it was a "myth" that the Turkish sea border could not be secured.
"We want to save Schengen, we want common European solutions, but the clock is ticking," said de Maiziere, adding that the key to solving the crisis was a deal with Turkey to staunch the flow of migrants.