Foreign Minister Sebastian Kurz said that unless Austria copied Germany and reintroduced border checks itself, the country would be "completely overwhelmed within a few days.
"We have to be aware that if we leave open (the borders), every day we will get 10,000 people who would then stay in Austria. Our geographical situation is that we are the last country, the last attractive target country, in the chain before Germany," Kurz said late yesterday.
There appeared to be a split in the Austrian government with Chancellor Werner Faymann - from a different party to Kurz - saying yesterday that there would be no systematic controls, only spot checks.
Overnight around 4,500 migrants entered Austria at the main border crossing point at Nickelsdorf with police saying they expected thousands more during today.
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A further 3,000 also crossed at Heiligenkreuz near Graz, where police said around 500 more were arriving every hour.
In recent weeks, tens of thousands of migrants have travelled up the western Balkans from Greece into Hungary and then Austria, all but a handful continuing to Germany - which has relaxed asylum rules for Syrians - and also Sweden.
A record 5,809 entered Hungary yesterday, police said today, smashing the previous day's record of 4,330.
Migrants told an AFP correspondent on the Hungarian border that buses were taking them straight to train station at Szeged to go to Budapest, and not to registration camp.