Austria saw the arrival of about 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 about 9,000 people had crossed the border from Hungary since midnight, about 5,000 at Heiligenkreuz, near the city of Graz, and 4,000 at Nickelsdorf near Vienna.
It expected at least 10,000 by the end of the day.
The deputy police chief of Austria's Burgenland state, Christian Stella, told Austria Presse Agentur 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.
One migrant who crossed into the Austrian town of Heiligenkreuz from Hungary told the Associated Press news agency: "I feel like I've been born anew. It makes no difference whether I am delayed, whether I stay here two days. The important thing is that I've finally arrived and that I am now finally safe."
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 Mr 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"