A Syrian girls rests on a platform next to a stuffed toy given by wellwishers after she arrived with her family on a train from Budapest's Keleti station at the railway station of the airport in Frankfurt, Germany, early morning Sept 6, 2015. [Photo/Agencies]

HEGYESHALOM, Hungary/MUNICH - Austria and Germany threw open their borders on Saturday to thousands of exhausted migrants from the east, bussed to the frontier by a right-wing Hungarian government that had tried to stop them, but was overwhelmed by the sheer numbers of people.

Left to walk the final stretch into Austria, rain-soaked migrants - many of them refugees from Syria's civil war - were whisked by train and shuttle bus first to Vienna and then by train to Munich and other cities in Germany.

The last train carrying an estimated 1,000 refugees pulled into Munich from Austria at 1:30 a.m. on Sunday (2330 GMT), bringing the total to have arrived in the Bavarian capital since Saturday to about 8,000.

Police immediately ushered the arrivals onto another train bound for Dortmund on the opposite platform, cordoned off from onlookers in the main station terminal.

Some who wanted to stay in Munich initially refused to get on the second train, which eventually set off with all the passengers about an hour later.

Most of those who arrived on Saturday were bussed to reception centres in and around the Munich after being medically screened, fed and offered fresh clothing. Many said they were from Syria, while others were from Afghanistan or Iraq.