By Krisztina Than and Karin Strohecker

HEGYESHALOM, Hungary/VIENNA (Reuters) - Austria and Germany threw open their borders to thousands of exhausted migrants on Saturday, bussed to the Hungarian border by a right-wing government that had tried to stop them but was overwhelmed by the sheer numbers reaching Europe’s frontiers.

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.

Germany said it expected to receive up to 10,000 on Saturday. Austrian police said 4,000 had crossed by the morning, but that many more were expected during the day as Europe’s asylum system buckled under the pressure of the continent’s worst refugee crisis since the Yugoslav wars of the 1990s.

"It was just such a horrible situation in Hungary," said Omar, arriving in Vienna with his family and hundreds of other migrants who poured out onto a fenced-off platform and were handed food, drinks and other supplies.

In Budapest, almost emptied of migrants by nightfall on Friday, the main railway station was again filling up with newly arrived migrants but trains to western Europe remained cancelled. So hundreds set off by foot, saying they would walk to the Austrian border like others had tried on Friday.

After days of confrontation and chaos, Hungary’s government deployed over 100 buses overnight to take thousands of migrants to the Austrian border. Austria said it had agreed with Germany that it would allow the migrants access, waiving asylum rules that require them to register in the first EU state they reach.

Wrapped in blankets and sleeping bags against the rain, long lines of weary migrants, many carrying small, sleeping children, climbed off buses on the Hungarian side of the border and walked into Austria, receiving fruit and water from aid workers. Waiting Austrians held signs that read, “Refugees welcome”.

“We’re happy. We’ll go to Germany,” said a Syrian man who gave his name as Mohammed. Another, who declined to be named, said: “Hungary should be fired from the European Union. Such bad treatment.”

Hungary's insisted the bus rides were a one-off, even as hundreds more migrants assembled in Budapest on Saturday, part of a seemingly relentless surge through the Balkan peninsula from Turkey and Greece.

Bavarian state police said they expected the first refugees to arrive in Germany around midday, with national rail operator Deutsche Bahn saying a special train with 500 refugees aboard due to reach Munich around lunchtime.

DESPERATE MIGRANTS FORCE HUNGARY'S HAND

Hungary, the main entry point into Europe’s borderless Schengen zone for migrants heading northwards through the Balkans, has taken a hard line, vowing to seal its southern frontier within days. Hungarian officials have painted the crisis as a defence of Europe’s prosperity, identity and “Christian values” against an influx of mainly Muslim migrants.

For days, several thousand camped outside Budapest’s main railway station, where trains to western Europe were cancelled as the government insisted all those entering Hungary be registered and their asylum applications processed in the country as per EU rules.

But on Friday, in separate rapid-fire developments, hundreds broke out of a teeming camp on Hungary’s frontier with Serbia, escaped a stranded train, and took to the highway by foot chanting “Germany, Germany!”

The government appeared to throw in the towel, ordering over 100 buses to take them to the border. Arriving at a Vienna railway station on Saturday, migrants were met by announcements for Germany-bound trains in Arabic as well as German.

The scenes were emblematic of a crisis -- about 350,000 refugees and migrants have reached the border of the European Union this year -- that has left the 28-nation EU groping for solutions amid sharp divisions over burden-sharing.

BOY'S BODY ON BEACH PRICKS EU'S CONSCIENCE

Pressure to take effective action rose sharply this week after pictures flashed around the world of the body of a 3-year-old Syrian Kurdish boy washed up on a Turkish resort beach, personalising the collective tragedy of the refugees. Aylan Kurdi had drowned along with his mother and brother while trying to cross by boat on a tiny rubber dinghy to a Greek island.

Hungary has lashed out at Germany, which expects to receive 800,000 asylum seekers this year, for declaring it would accept Syrian requests regardless of where they enter the EU, contrary to the bloc's rules.

Budapest says this has swelled the influx, and like some others in ex-Communist east European states -- unused to taking in notable numbers of foreigners -- it is resisting calls by some western EU leaders for each of the bloc’s 28 members to accept a quota of refugees. The discord continued on Saturday.

“What happened is the consequence of the failed migration policy of the European Union and the irresponsible statements made by European politician,” Hungarian Foreign Minister Peter Szijjarto said on arrival at a meeting of EU foreign ministers in Luxembourg to discuss the migration crisis.

Polish Prime Minister Ewa Kopacz reiterated on Saturday that Warsaw was prepared to accept 2,000 migrants. “We are committed to solidarity, but it has to be a responsible solidarity.”

The flow of migrants risking rickety boats to cross the Mediterranean, or baton-wielding police on Balkan borders, shows no sign of abating despite more trips by sea ending in disaster.

Over 2,000 have died at sea so far this year, including 30-40 on Friday who were reported drowned off Libya's coast.

A record 50,000 hit Greek shores in July alone and were ferried from islands unable to cope to the mainland by a government already floundering in financial crisis and keen to dispatch them promptly north into Macedonia, whence they enter Serbia and then Hungary.

Hungary said on Saturday it had recorded some 165,000 entering so far this year. Countless others may have crossed its borders without registering.

Determined to stem the tide, Hungary is building a 3.5-metre (11.5-foot) high fence along its border with Serbia. On Friday, the Budapest parliament adopted measures the government says will effectively seal the frontier to migrants as of Sept. 15.

They include “transit zones” on the border, where asylum seekers would be held until their requests are processed and, if denied, they would be deported.

 

(Additional reporting by Sandor Peto and Balazs Koranyi in Budapest, Shadia Nasralla in Alpbach, Austria and Thomas Seythal in Berlin; Writing by Matt Robinson; Editing by Mark Heinrich)