Austrian Foreign Minister Sebastian Kurz, whose country has set a refugee cap of 37,500 for this year, said the European Union did not seem to fully realise "how serious the situation is."
"I say this very clear -- if we do not manage to control the situation... our only option will be to cooperate with Slovenia, Croatia, Serbia, Macedonia," Kurz said after an informal meeting of EU foreign ministers in Amsterdam.
More than a million migrants, mostly Syrians fleeing their war-torn country, landed in the 28-nation European Union last year, most of them crossing into Greece from Turkey, and then making their way through the Balkans to Germany and other northern member states.
The influx has exposed sharp differences and called into question the future of the Schengen passport-free zone as several countries -- among them Germany, Austria, Hungary, Sweden -- have re-introduced border controls.
Despite repeated efforts to halt the inflow, several thousand people a day still make the dangerous trip from Turkey to Greece and an upsurge in fighting in Syria threatens to make the problem even worse.
Foot the bill
Fanning the controversy, Austria media quoted Austrian Finance Minister Hans Jörg Schelling as demanding Brussels foot a bill Vienna estimates at 600 million euros ($670 million) for Austria taking in some 90,000 asylum seekers last year, saying his country could only afford to pay for 35,000.
The Kurier daily reproduced part of a letter to that effect which Schelling sent on January 25 to EU Commission President Jean-Claude Juncker.
The finance ministry was not immediately available for comment.
Hungarian Foreign Minister Peter Szijjarto said separately that the EU was "defenceless from the south."
"If Greece is not ready or able to protect the Schengen zone ... then we need another defence line, which is obviously Macedonia and Bulgaria," Szijjarto said.
Hungary has taken the lead in calls for erecting a fence along Greece's northern border in the same way it built a razor-wire barrier along its own southern frontier last year.
Athens says it is doing its best but the numbers have overwhelmed the resources of a small country which is also struggling to get its economy back on track after a third debt bailout was agreed last year.
Earlier this week, the EU said Greece had to remedy a series of failings in order to re-establish full control over the border with Turkey and so preserve the Schengen area, prized as one of the bloc's greatest achievements.
If Greece failed to comply, then Brussels could allow other member states to extend border controls for up to two years, an option officials say they want to avoid at all costs.