In midweek, Greece's top migration official slammed a report in the Financial Times alleging several European ministers and senior EU officials believe threatening suspension from Schengen could persuade Greece to protect its borders more effectively.
Junior interior minister for migration Yiannis Mouzalas said the report contained "falsehoods and distortions" but Mikl-Leitner said temporary exclusion was a real possibility.
"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," Mikl-Leitner said in an interview with German daily Die Welt.
"It is a myth that the Greco-Turkish border cannot be controlled," Mikl-Leitner insisted.
"When a Schengen signatory does not permanently fulfil its obligations and only hesitatingly accepts aid then we should not rule out that possibility," she added.
"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," she insisted.
Germany's Steinmeier criticised Vienna's warning however.
"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."
'Make or break'
International Monetary Fund chief Christine Lagarde added her voice to Schengen concerns when she said the refugee crisis had pushed Europe to a "make or break" point.
"The refugee crisis is a bit of a make or break, from my personal perspective," Lagarde said at the World Economic Forum in the Swiss ski resort of Davos. Asked if it endangered Schengen, she said: "Yes, I think so."
Cash-strapped Greece has for months come in for criticism from its EU partners on its attempts to manage the largest flow of migrants in decades as hundreds of thousands flee war and repression.
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Many of the migrants have reached Greek islands from nearby Turkey after perilous sea voyages before streaming further north, with many targeting a new life in Germany, Europe's economic powerhouse.
The EU last month 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 came to the fore once again with Wednesday's FT report.
A spokesman for Greek Prime Minister Alexis Tsipras denied the EU made any threat to that effect.