Austria and Germany have thrown open their borders to thousands of exhausted migrants.

They were bussed to the Hungarian border by the right-wing government that had tried to stop them but was ultimately overwhelmed by the sheer numbers of people reaching Europe.

Left to walk the last yards into Austria, rain-soaked migrants, many of them refugees from Syria's civil war, were whisked by train and shuttle bus to Vienna, where many said they were resolved to continue on to Germany.

"Because we heard Germany probably accepts all the migrants who were in Budapest. They will let them all there in Germany. I'm not sure but somehow like that," an Afghan refugee said.

Austrian police said 4,000 had already crossed by the morning, but that many more were expected during the day.

Germany said it expected to receive up to 10,000 people from the first wave of migrants, as Europe's asylum system buckled under the pressure of the continent's worst refugee crisis since the Yugoslav wars of the 1990s.

More than 140,000 migrants have been recorded entering Hungary so far this year through the EU's external border with Serbia. Countless others may have entered without registering.

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