The first train carrying 167 migrants from Austria to Germany has arrived in Munich.
As many as 10,000 refugees are expected to arrive in the country today, police said.
German police say they are expecting up to 10,000 refugees coming from Hungary via Austria today.
Around 4,000 refugees have now reached the Austrian border after being bussed there from Hungary.
Austrian Police spokesman Helmut Marban said the final numbers "could double, if not more".
On top of 20 buses shuttling back and forth between Vienna and Hungary, a special half-hourly train service has also been put on.
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."
It'll be largely dry and bright across many parts today with plenty of sunny spells, particularly in the north.
The remnants of a weak front with patchy rain and drizzle will clear the far south through the first part of the morning with cloud breaking up behind.
It will feel cool with the northwesterly breeze persisting, keeping temperatures down to a maximum of 18C (64F).
Passengers on one of the country's busiest rail lines were forced to deal with hours of delays as a knock-on effect of cable theft.
Customers on the Virgin Trains East Coast main line were informed on the tannoy system that the disruption was caused by the "vandalism" at Darlington which in turn caused signalling problems.
Some services were replaced by buses, while on others passengers were delayed by up to 60 minutes even after the problem had been fixed.
Anyone delayed by more than 30 minutes can apply for compensation via the Virgin Trains website, the operator said.