BUDAPEST, Hungary » For weeks while they traveled a punitive road, Europe cast a cold eye on their unwelcome progress. On Saturday, for the first time since fleeing their troubled homelands, they could set foot in their promised land — and it came with a German face so friendly that it brought some newcomers to tears of joy.

More than 7,000 Arab and Asian asylum seekers surged across Hungary’s western border into Austria and Germany following the latest erratic policy turn by Hungary’s immigrant-averse government. Within hours, travelers predominantly from Syria, Iraq and Afghanistan who had been told for days they could not leave Hungary were scooped from roadsides and Budapest’s central train station and placed on overnight buses, driven to the frontier with Austria and allowed to walk across as a new day dawned.

They were met with unexpected hospitality featuring free high-speed trains, seemingly bottomless boxes of supplies, and well-wishers offering candy for everyone and cuddly toys for the children in mothers’ arms. Even adults absorbed the sudden welcome with a look of wonderment as Germans and Austrians made clear that they had reached a land that just might become a home.

"I’m very glad to be in Germany. I hope that I find here a much better life. I want to work," said Homam Shehade, a 37-year-old Syrian shopkeeper who spent 25 days on the road. He left behind his parents, a brother, wife, a 7-year-old boy and a 2 ½-year-old girl. He hopes to bring them all to Germany. Until then, he said: "I hope that God protects them from the planes and bombs. My shop was bombed and my house was bombed."

As the migrants departed Hungary, leaders took a few final swipes at their departing guests.

Prime Minister Viktor Orban told reporters that Hungary drove the migrants to the border only because they were posing a public menace, particularly by snarling traffic and rail lines west of Budapest when they mounted a series of surprise breakouts from police-controlled positions Friday and headed for Austria on foot.

Orban said the people being taken by Germany mostly come "from regions that are not ravaged by war. They just want to live the kind of life that we have. And I understand that, but this is impossible. If we let everybody in, it’s going to destroy Europe."

Orban said Hungary was determined to staunch the flow of foreigners traversing the country. He criticized European Union plans to reach a bloc-wide agreement at a summit Sept. 14 committing each nation to accept higher quotas of foreigners to shelter, arguing that this would only spur more one-way traffic.

"What will it solve if we divide 50,000 or 100,000 migrants among us, when uncountable millions will be on the way?" Orban said.

A central Budapest rally by Hungary’s third-largest party, the neo-fascist Jobbik, underscored why many of those seeking sanctuary in Europe wanted to get through the country as quickly as possible. Earlier in the week, many of the same Jobbik activists traveled south to the border with Serbia to hurl verbal abuse at newly arrived travelers.

Jobbik leader Gabor Vona told the crowd of 300 waving Hungarian and party flags "that Hungary belongs to the Hungarians. We like everybody, we respect everybody — but we don’t want anybody coming here."

Other speakers branded supporters of refugee rights "traitors" and "scum."

The contrast could not have been greater in Vienna’s central train station. When around 400 asylum seekers arrived on the morning’s first border train, charity workers offered food, water and packages of hygiene products for men and women. Austrian onlookers cheered the migrants’ arrival, with many shouting "Welcome!" in both German and Arabic. One Austrian woman pulled from her handbag a pair of children’s rubber rain boots and handed them to a Middle Eastern woman carrying a small boy.

Sami Al Halbi, a 28-year-old veterinarian from Hama in Syria, said he fled to avoid mandatory military service. "They asked me to join the army. I am educated. For years I’ve been holding a pen. I do not want to hold a weapon," he said. "We all want to have a better future."

It got better as travelers continued west on more trains, some of them specially provided for the migrants. As Austria’s government noted, virtually none of those coming intended to seek asylum before reaching Germany, the Eurozone powerhouse that has pledged to aid Syrians fleeing from their 4-year-old civil war. Germany expects to receive a staggering 800,000 asylum seekers this year.

In Munich’s central station, the first arrivals from Hungary received cheering and applause. Many who had endured nights sleeping on crowded concrete floors at Budapest’s Keleti station appeared disoriented as Germans approached them holding trays of food. The youngest brightened up as teddy bears were offered as gifts.

"We are giving a warm welcome to these people today," said Simone Hilgers, spokeswoman for Upper Bavaria government agencies tasked with providing the migrants immediate support. "We realize it’s going to be a big challenge but everybody, the authorities and ordinary citizens, are pulling together."

A total of about 6,000 people had come through Munich by Saturday evening, Hilgers said. All were given food and drink, and most were housed in temporary accommodation.

The latest arrivals add to the tens of thousands of migrants who have been streaming each month into Germany, the EU’s most populous nation with 81 million residents. The influx has strained emergency accommodation and local bureaucracy, triggered sporadic violence by neo-Nazi extremists, and inspired empathy from many more Germans. Volunteer groups have sprung up to help asylum seekers find permanent housing and jobs, and to receive free German language lessons. German media estimate this year’s expected bill for providing sanctuary to be 10 billion euros ($11 billion), should the forecast 800,000 arrive.

Germany typically places newcomers in housing earmarked for asylum seekers. They are provided free meals, clothing, health care and household support, as well as monthly spending money averaging 143 euros ($160). After three months, they receive restricted work opportunities. By contrast, the migrants left behind a Hungary that stuck them in sweltering outdoor facilities on the Serbian border, left any aid to private charities, and pocketed the money the migrants paid to buy cross-border train tickets that they were blocked from using.

Hungary announced Saturday morning that its emergency bus services to the border had finished and would not be repeated. Almost immediately, two new groups started long walks to the border: about 200 people who walked out of an open-door refugee camp near the city of Gyor, and about 300 who left Keleti station. Hundreds more made their way west independently, on foot and by train.

Jordans reported from Berlin. Associated Press reporters Paul Wheatley in Munich, Germany; Marko Drobnjakovic, Pablo Gorondi and Alexander Kuli in Budapest; Balint Szlanko and Petr Josek in Nickelsdorf, Austria, and George Jahn in Vienna contributed to this report.