Around 2,000 refugees have arrived at the Austrian border from Hungary so far, Austrian police say, adding that the number could more than double by the end of Saturday.
Hans Peter Doskozil, chief of police in the Austrian province of Burgenland, said two special trains had been arranged to take migrants from the border town of Nickelsdorf to the capital Vienna, after they had been brought by bus by Hungarian authorities.
However, he claimed that Hungary was refusing to let Austrian buses enter Hungary to pick them and deliver them to the trains, meaning they had to walk in rain and darkness.
"Our biggest problem is that the Hungarians - after checking back with Budapest - are refusing to let our buses enter their territory and pick up the refugees," he said.
He added: "We offered them that they can bring the refugees directly to the trains, or to the shelter [on the Austrian side], but they just stop the buses on the Hungarian side, everyone has to get off in the rain."