Migrants stand outside a train at the railway station in the town of Bicske, Hungary, September 3, 2015. [Photo/Agencies]

VIENNA - Migrants arriving in Vienna from Hungary will not be checked or registered and can continue their onward journeys across Europe, the police chief in Austria's capital said on Thursday as another wave of westward-bound travellers boarded trains from neighbouring Hungary.

Vast numbers of people arriving from countries in war or poverty, especially from Syria, are confronting Europe with its biggest refugee crisis since World War Two. Many are pouring through Hungary and Austria en route to Germany.

Migrants hoping to travel to western Europe streamed into Budapest's main railway station on Thursday, with hundreds storming a train after Hungarian police withdrew following a two-day standoff, triggering chaotic scenes.

Austrian rail operator OeBB said a number of trains had left Budapest for Sopron, which is near the Austrian border and connected to Vienna via regional rail lines. No intercity trains were running from Budapest to Vienna, unlike on Tuesday when migrants packed trains hoping to make it to Germany or beyond.

"What we certainly can't do is check all those people coming through, establish all their identities, or possibly even arrest them -- we can't do this, and we have no plans to do this," Vienna police chief Gerhard Puerstl told reporters.

Asked if the migrants would be allowed to continue their journey, Puerstl said "Yes - of course, we will ensure that everything is orderly, there is no question of that," adding there was no point in shuttling people back and forth in trains.