Vienna`s announcement prompted sharp criticism from Berlin, underlining how the crisis is straining relations within the EU.
The Schengen passport-free area is seen as one of the EU`s most important achievements and the Commission has repeatedly expressed concern that re-imposing border controls threatens its future.
"We do not believe that the current migrant crisis that Europe is facing can be resolved with the building of fences or walls," German government spokesman Steffen Seibert said.
EU officials said they were not told in advance of Austria`s plan and in a sign of the sensitivity of the development, European Commission President Jean-Claude Juncker held hastily arranged talks with Austrian Chancellor Werner Faymann.
Afterwards the two men issued a statement apparently seeking to stress common ground..
"The president and the chancellor repeated their common position that fences have no place in Europe," the statement said.
Just days ago, Juncker and other EU leaders at an emergency Balkans summit warned that "unilateral actions could trigger a chain reaction".
Slovenia -- another Schengen country -- also reiterated its readiness to erect a fence along its Croatian frontier if new EU plans aimed at improving the situation failed to produce quick results.
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