"I am standing right at the border to Hungary and am looking down. The streams [of people] keep coming," AFP cited Hans Peter Doskozil, chief of police in Burgenland state as telling the Austria Press Agency.
"We are waiting for 17 or 18 double-decker buses to be able to take people to Vienna, maybe also towards Germany," he said.
One train carrying around 400 migrants westwards has already left the Austrian town of Nickelsdorf on the border with Hungary and a second one with around the same number is due to leave soon, Doskozil said.
The first 400 trudged from a concert hall that is now a makeshift shelter in Nickelsdorf to the train station at around 4:30-5:30 am (0230-0330 GMT).
"The second 400 are on their way their now. At times the rain has been really heavy, now it's drizzling a bit. The people are all soaked," Doskozil said.