At least 10,000 refugees have arrived in Austria on September 19, amid bitter rows among EU nations on how to handle the growing crisis.
The refugees had been sent from Croatia into Hungary, which in turn shipped them on to Austria.
Hungary accused Croatia of breaking the rules by failing to register the refugees.
Meanwhile, 26 refugees are missing after their boat sank off Greece.
Separately, a search is continuing for 13 people still missing after their boat sank in the same waters on September 19, killing a five-year-old girl.
On the same day, 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 neighboring countries of failing to follow EU rules, expressing concern that migrants were also arriving from Croatia via Slovenia.
One refugee, who crossed into the Austrian town of Heiligenkreuz from Hungary, told the Associated Press: “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 refugees entering from Serbia since September 16 and, after initially welcoming them, said it was unable to cope and moved them on.
PM 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 Zoran 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 refugees and said all asylum seekers would be registered in Hungary before they could leave for northern Europe.
However, a number of refugees who reached Austria via Hungary ssaid 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.
While Hungary continues to transport refugees arriving from Croatia, it is building a razor-wire fence on the border that will be completed soon.
Hungary 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”.