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 authorities promptly arranged for thousands to head straight on to Germany.

German police said the first 1,000 of up to 10,000 migrants expected on Saturday had arrived on special trains in Munich. Austrian police said over 6,000 had entered the country by midday with more expected in what has become Europe’s most acute refugee crisis since the Yugoslav wars of the 1990s.

Munich police said Arabic-speaking interpreters helped refugees with procedures at emergency registration centers. The seemingly efficient Austrian and German reception contrasted with the disorder prevalent in Hungary.

"It was just such a horrible situation in Hungary," said Omar, arriving in Vienna with his family.

In Budapest, almost emptied of migrants the night before, the main railway station was again filling up with new arrivals but trains to western Europe remained canceled. So hundreds set off by foot, saying they would walk to the Austrian border, 170 km away, 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 frontier. Austria said it had agreed with Germany to 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, got off buses on the Hungarian side of the boundary 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, naming Europe's famously biggest and most affluent economy that is the favored destination of many refugees. Another, who declined to be named, said: “Hungary should be fired from the European Union. Such bad treatment.”

Hungary insisted the bus rides were a one-off, even as hundreds more migrants gathered in Budapest, part of a seemingly unrelenting human surge northwards through the Balkan peninsula from Turkey and Greece.

By contrast, the Austrian state railway company OeBB said it had added 4,600 seats for migrants by extending trains and laying on special, non-scheduled services.

Hungary, the main entry point into Europe’s borderless Schengen zone for migrants, has taken a hard line, vowing to seal its southern frontier with a new, high fence by Sept. 15.

Hungarian officials have portrayed the crisis as a defence of Europe’s prosperity, identity and “Christian values” against an influx of mainly Muslim migrants.

Prime Minister Viktor Orban said on Saturday Hungary would deploy police forces along its border with Serbia after Sept. 15 and the army too if parliament approves a government proposal.

"It’s not 150,000 (migrants coming) that some (in the EU) want to divide according to quotas, it’s not 500,000, a figure that I heard in Brussels, it’s millions, then tens of millions, because the supply of immigrants is endless," he said.

For days, several thousand camped outside Budapest’s main railway station, where trains to western Europe were canceled as the government insisted all entering Hungary be registered with asylum applications processed there as per EU rules.

But the logjam broke on Friday when, 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, mobilizing a fleet of buses to take them to the Austrian border.

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 dysfunctional squabbling over burden-sharing.

At an EU foreign ministers meeting in Luxembourg on Saturday, the usual diplomatic conviviality unraveled as they failed to agree on any practical steps out of the crisis. They are especially at odds over proposals for country-by-country quotas to take in asylum seekers.

"Given the challenges facing our German friends as well, all of Europe needs to wake up. (The time for) reverie is over," Austrian Interior Minister Johanna Mikl-Leitner said.

"Now the continent of Europe is challenged. In this great challenge the entire continent has to give a unified answer. Whoever still thinks that withdrawal from the EU or a barbed wire fence around Austria will solve the problem is wrong."

British finance minister George Osborne said Europe and Britain must offer asylum to those genuinely fleeing persecution but also need to boost aid, defeat people-smuggling gangs and tackle the conflict in Syria to ease the migrant crisis.

Pressure to take effective action rose sharply this week after pictures flashed around the world of the body of a three-year-old Syrian Kurdish boy washed up on a Turkish resort beach, personalizing 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.

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 politicians,” Hungarian Foreign Minister Peter Szijjarto said on arrival at the Luxembourg meeting.

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.

The Greek coastguard said on Saturday that about 13,370 migrants and refugees had been ferried from Greece's eastern islands to Athens since Monday.

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.

Determined to stem the tide, Hungary is building a 3.5-metre 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.-Reuters