"We are still in the process of verifying how many of them are actually asylum-seekers," Austrian police spokesman Patrick Maierhofer told AFP.
Many of the migrants slept at Vienna's Westbahnhof station, hoping to continue their journey on to Germany, which last week eased asylum restrictions for Syrian refugees.
Europe is on the receiving end of the biggest movement of people since World War II, with more than 300,000 arriving this year, many fleeing war, persecution and poverty in the Middle East and Africa.
The escalating crisis has divided the 28-member bloc ahead of fresh emergency talks on September 14, with Western European leaders calling for more efforts to help the new arrivals while countries on its eastern borders say they are struggling to cope.
In a show of support for the migrants, 20,000 people took to the streets of Vienna on Monday evening to protest their ill-treatment, while senior government officials attended a church service for 71 refugees found dead in an abandoned truck last week.
Hungary's government criticised Berlin's easing of asylum rules -- aimed at relieving pressure on southern European nations where migrants arrive by sea -- as "(building) up the hopes of illegal immigrants".
Under current EU regulations, known as the Dublin provision, asylum-seekers must remain in the first European country they enter while their application is being processed.
Those who subsequently travel to other member states face deportation back to the EU country they originally entered.
Hungary has become a frontline country for migrants arriving via the western Balkans route as they flee war and unrest in the Middle East, Africa and Asia.
The Hungarian government on Monday demanded that Berlin clarify "the legal situation, in order to eliminate this ambiguity and controversy".
"It is in our common interest that all member states abide by EU legislation. Order and legality must be restored at the borders of the European Union", said government spokesman Zoltan Kovacs