Greece faced mounting pressure from other EU countries on Monday to get a better handle on migration flows, but suggestions that the country could be excluded from Europe's border-free Schengen area faced resistance.
More than 1 million migrants and refugees reached Europe last year, straining local resources and creating tensions between European countries.
EU interior ministers were meeting in Amsterdam on Monday to discuss their response to the refugee crisis, most notably when it comes to border controls.
Currently, most migrants travel from Turkey to Greece and on through the Balkans to reach northern European nations. Greece has been accused of letting the migrants move through its territory largely unchecked, even though it is supposed to police its border with Turkey.
Turkey is one of the external frontiers of the Schengen area, a free-travel zone that allows people to move around freely through 26 European countries, normally without the need for passports or border checks.
"If people do not manage to secure the European external borders - that is the Turkish-Greek border - then the external Schengen border will move back towards Central Europe," Austrian Interior Minister Johanna Mikl-Leitner threatened Monday, ahead of the Amsterdam talks.
"Greece is required here to do everything as quickly as possible, to use resources ... to secure this external border," she added. "It is a myth to think that the Greek-Turkish border cannot be secured. The Greek navy has sufficient capacities to protect this border."
German Interior Minister Thomas de Maiziere told journalists in Amsterdam that pressure would be put on Athens so that "Greece does its homework."
"We need to look very closely at the position of Greece within Schengen," Belgian Interior Minister Jan Jambon added. "First and foremost, Greece has to do what it has to do - namely controls."
But the European Commission rejected the suggestion that Greece could be excluded from the 26-country Schengen area.
"There is no plan to exclude Greece from anything. We never discussed either a suspension of Schengen, or the exclusion of a Schengen member," said Natasha Bertaud, a spokeswoman for the European Union's executive.
Greek Deputy Immigration Minister Ioannis Mouzalas complained Monday about the "blame game" against Athens, arguing that the country is becoming "better and better" at identifying migrants upon arrival.
Meanwhile, several EU ministers warned about the risk of chipping away at the unity of the Schengen bloc.
"In no case should we abandon Schengen, it is really the be-all and end-all of the EU," said Luxembourg Deputy Prime Minister Etienne Schneider.
"Europe must remain a stable structure ... There cannot be bits of Europe inside and bits of Europe outside because that would be the start of dissolution," Italian Interior Minister Angelino Alfano added.
Speculation is rife, however, that Schengen's free-travel principle is already at risk of crumbling after some member states re-introduced internal border controls to stem refugee flows.
The EU ministers were considering ways Monday of prolonging those emergency measures.
"Schengen and freedom of movement is one of the biggest achievements of European integration. We have to do all that is possible to safeguard it," EU Migration Commissioner Dimitris Avramopoulos said in an interview with the Italian daily Il Messagero published Monday.
"The refugee crisis today is threatening something bigger than simply the Schengen treaty," he added. "European unity as a whole is at stake."