Austria says it is planning to phase out special measures that have allowed thousands of migrants to travel freely from Hungary to Western Europe.
Chancellor Werner Faymann said Austria would remove the emergency measures for asylum seekers "step by step".
The easing of rules has meant thousands have been able to leave Hungary for Austria and Germany over the weekend.
Germany, where most of the migrants are heading, warned that its willingness to help "should not be overstretched".
Amid sharp disagreements among EU members, the UN's Refugee Chief said the crisis was "manageable" if member states could agree a joint plan.