Austria saw the arrival of at least 10,000 migrants on Saturday, amid bitter rows among EU nations on how to handle the growing crisis.
The migrants were initially sent into Hungary by Croatia, which said it was unable to cope with the 20,000 who had arrived since Wednesday.
Hungary in turn shipped them on to Austria, accusing Croatia of breaking rules by failing to register migrants.
However, some told the BBC that Hungary had not registered them either.
On Saturday Austrian police said they were expecting at least 10,000 arrivals, while the head of the Austrian Red Cross, Gerry Foitik, later told Austria Presse Agentur (APA) that between 12,000 to 13,000 people had entered the country over the course of the day.
The deputy police chief of Austria's Burgenland state, Christian Stella, told APA that Hungary had not given enough warning.
Austrian Interior Minister Johanna Mikl-Leitner accused neighbouring countries of failing to follow EU rules, expressing concern that migrants were also arriving from Croatia via Slovenia.
Croatia has seen 20,000 migrants entering from Serbia since Wednesday and after initially welcoming them said it was unable to cope and moved them on.
Prime Minister Zoran Milanovic admitted there was no agreement with Hungary.
"We forced them, by sending people up there. And we'll keep doing it," he said.
Hungarian Foreign Minister Peter Szijjarto branded Milanovic "pathetic", adding: "Instead of honestly making provision for the immigrants, it sent them straight to Hungary. What kind of European solidarity is this?"
The Hungarian government accused Croatia of breaching international law by failing to register migrants and said all migrants would be registered in Hungary before they could leave for northern Europe.
However, a number of migrants who reached Austria via Hungary told the BBC they had not been registered in Hungary either, simply driven in buses across the country and told to walk over a railway line into Austria.
A Hungarian government spokesman could not confirm this, but said that although it was policy to register migrants, they could not be forced to do so.
While Hungary continues to transport migrants arriving from Croatia, it is building a razor-wire fence on the border that will be completed soon.It says it will then enforce the same tough laws it introduced earlier this week on its Serbian border - where there is a similar fence - making crossing it a criminal offence.
However, government spokesman Zoltan Kovacs said that "at the moment" stopping the flow "seems to be impractical".
In other developments:
--A five-year-old girl died when the boat taking her from Turkey to the Greek island of Lesbos sank, the Greek coastguard said. At least 13 other migrants on board are missing
--A series of multinational operations off Libya, including vessels from the UK, Italy and Germany, rescued nearly 5,000 people trying to reach Europe
--Romanian Foreign Minister Bogdan Aurescu says Hungary's plan to build a fence along their shared border is an "unacceptable solution and it contravenes the spirit of the EU"
Slovenia also accused Croatia of breaking the rules of both the EU and the Schengen free movement area.
It said more than 1,500 migrants had entered the country, with hundreds more at the border.
Slovenian interior ministry official Bostjan Sefic said the police were "fully in control and the security situation is good".
Some 150 migrants have now entered Austria from the Slovenian border and were taken to the southern Austrian town of Spielfeld.
Most of the migrants are en route to more prosperous northern European countries - with Germany the favourite destination.
The EU has been strongly criticised for its failure to co-ordinate a response.
Interior ministers will hold an emergency meeting on Tuesday in another attempt to agree on relocating migrants with binding quotas for each state.
The next day, EU leaders will hold an extraordinary summit on migration.