Austria has warned Greece that it could face "temporary exclusion" from the European Union (EU)'s passport-free Schengen zone if it fails to tighten controls on its borders and stop the flood of refugees.

"If the Athens government does not finally do more to secure the [EU's] external borders, then one must openly discuss Greece's temporary exclusion from the Schengen zone," Austrian Interior Minister Johanna Mikl-Leitner said in an interview with German daily Die Welt on Saturday.

"It is a myth that the Greco-Turkish border cannot be controlled,” she added.

Europe is facing an unprecedented influx of refugees who are fleeing conflict-ridden zones in Africa and the Middle East, particularly Syria. Damascus blames foreign support for militants wreaking havoc in the country for the refugee crisis. 

Over one million refugees, mostly from crisis-hit countries in the Middle East and North Africa, entered Europe in 2015. According to the reports, the vast majority of the refugees first entered the continent through Greece after dangerous sea voyages from Turkey before heading north, with many trying to reach Europe's economic powerhouse, Germany.

Mikl-Leitner stressed that the temporary exclusion of the cash-strapped country is a real possibility, “when a Schengen signatory does not permanently fulfill its obligations and only hesitatingly accepts aid.”

"The patience of many Europeans has reached its limit... We have talked a lot, now we must act. It is about protecting stability, order and security in Europe," Mikl-Leitner added.

Earlier, Greece criticized a Wednesday report by Financial Times (FT) that said several European ministers and senior EU officials believed the threat of suspension from Schengen could convince Athens to protect its borders more effectively.

Greece's Junior interior minister for migration Yiannis Mouzalas said the report contained “falsehoods and distortions.”

Meanwhile, Germany’s Foreign Minister Frank-Walter Steinmeier slammed Austria’s warning, describing it a “pseudo-solution.”

“There won’t be any solution to the refugee crisis if solidarity disappears,” he said.

“On the contrary, we must work together and concentrate all our efforts to fight against the causes that are pushing the refugees into flight, to reinforce the EU’s outer borders and to achieve a fair redistribution [of asylum seekers] within Europe.”

Last month, the EU ruled out excluding Greece from Schengen, with Luxembourg’s Minister of Immigration Jean Asselborn observing that “it is not legally possible to exclude a state from the Schengen zone.”

But the issue surfaced once again with the FT report.

This comes as a spokesman for Greek Prime Minister Alexis Tsipras has denied that the EU made any threat to that effect.