Trainloads of migrants arrived in Austria and Germany from Hungary on Monday, August 31 as European Union asylum rules collapsed under the strain of a wave of migration unprecedented in the EU, Reuters reports.

As thousands of men, women and children - many fleeing Syria's civil war - continued to arrive from the east, authorities let thousands of undocumented people travel on towards Germany, the favored destination for many.

The influx is a crisis for the European Union, which has eliminated border controls between 26 "Schengen area" states but requires asylum seekers to apply in the first EU country they reach - something that is often ignored as migrants race from the fringes of the bloc to its more prosperous heart.

In line with EU rules, an Austrian police spokesman said only those who had not already requested asylum in Hungary would be allowed through - but the sheer pressure of numbers prevailed, and trains were allowed to move on.

"Thank God nobody asked for a passport ... No police, no problem," said Khalil, 33, an English teacher from Kobani in Syria. His wife held their sick baby daughter, coughing and crying in her arms, at the Vienna station where police stood by as hundred of migrants raced to board trains for Germany.

Khalil said he had bought train tickets in Budapest for Hamburg, northern Germany, where he felt sure of a better welcome after traipsing across the Balkans and Hungary.

"Syrians call (Chancellor Angela) Merkel 'Mama Merkel'," he said, referring to the German leader's relatively compassionate response so far to the migrant crisis.

Late on Monday, a train from Vienna to Hamburg on which migrants were traveling was met in Passau, Germany, by police wearing bullet-proof vests, according to a Reuters witness.

Police entered the train and migrants were asked to accompany them to be registered. About 40 people were seen on the platform.

Police said they would be taken to a police station for registration.