Asylum seekers whose journey had been slowed by bickering among Balkan countries began to arrive in Austria en masse Sunday, just one border away from the ultimate destination for many refugees, Germany.

Thousands of economic migrants and war refugees walked across the border from Hungary into Austria on Sunday, while hundreds more crossed from Slovenia.

About 15,000 were expected to arrive in Austria from Hungary at the Nickelsdorf border crossing this weekend, one of several gateways, the Austrian news agency APA reported.

In the Austrian border village of Spielfeld, asylum seekers arrived on foot from Slovenia without showing papers. After resting a few hours at an aid station, where local volunteers offered food, drink and new sneakers, the bedraggled travelers continued walking to the train station.

Austrian officials, who last week warned that they had reached their limit — with 20,000 beds in shelters filled — appeared to relax border controls. The wave of asylum seekers crossing into eastern Austria will be at Germany’s door by Monday afternoon.

“No documents, no photos, no fingerprints,” said Mirazi, who was waved through the border crossing here with his wife, Roshan, and their three young children.

For them, Austria marked the journey’s end after 13 days on the road, from the shell-shocked city of Kobane on the Syrian border with Turkey, which was heavily damaged in months of street fighting between Islamic State militants and Kurdish militias, to this bucolic Austrian village with guest houses tucked into the forested hills.

The couple planned to seek asylum in Austria, where Roshan’s sister lives with her husband. They spoke on the condition that their last names not be used because they worried about family left behind.

The family was prepared to walk the 12 miles into Austria from the Slovenian military camp where they spent Saturday night, but sympathetic locals, seeing the children, pulled over and offered them a lift. Most men making the same journey did so by foot.

They arrived at a row of white tents erected the day before in parking lots. A handful of Austrian soldiers stood at a distance, wearing only sidearms and no riot gear. After resting for an hour, they walked a mile to the train station. They were trying to contact family members to get the spelling of the name of the Austrian town where they wanted to go.

But many will travel on to Germany, which was expecting two trains carrying about 1,000 migrants and refugees to arrive Sunday night from Austria. Five more trains, each carrying about 500 people, are scheduled to arrive Monday through the border crossing between Salzburg, Austria, and the German town of Freilassing.

Separately, a building in Wertheim, near Frankfurt, that was designated an asylum shelter for 400 people was destroyed in an arson attack Sunday morning, underlining the strong resistance among some parts of the population to accepting the newcomers.

Austria’s neighbors have apparently realized that they cannot stem the tide and are now dealing with the crisis by shoveling people through their countries to continue their journey westward.

This strategy was working well Sunday: Croatia continued to send trainloads of people from Tovarnik, where migrants and refugees are arriving from Serbia, to Hungary and Slovenia, which are both part of the European Union’s passport-free Schengen zone. Hungary was ferrying the arrivals directly to the border with Austria.

This level of cooperation marks a departure from the sharp words of recent days, since Hungary sealed its border with Serbia, forcing refugees to re-route through Croatia. A country of 4.4 million people, Croatia has received 27,000 refugees since Wednesday.

But this is only a stop-gap measure for Europe, which is facing its biggest wave of migration since World War II.

Slovenian Prime Minister Miro Cerar told The Washington Post that his small country was overwhelmed and that other European leaders must seek a way to stop the mass migration closer to the source in Turkey and Greece.

The E.U. is scheduled to hold an emergency meeting Wednesday to discuss the humanitarian crisis, and in particular whether each member country should have a quota of refugees it must accept, as Angela Merkel, the German chancellor, wants.

Austria, meanwhile, has been insisting that refugees cannot choose their countries of asylum, passing through the Balkan countries on their way more prosperous northern ones.

Under E.U. rules, refugees must submit their asylum claims in the first E.U. country they enter.

The International Organization for Migration said last week that about 474,000 people have arrived in Europe this year, making often-treacherous journeys in dinghies across the Mediterranean Sea from Turkey to Greece, then making their way onward. The vast majority want to reach Germany, which anticipates receiving 800,000 asylum seekers this year.

They are now racing against the weather, trying to make the journey across the Mediterranean before the winter weather.

At least 13 people, including four children, died Sunday when the inflatable dinghy carrying them from Turkey to Greece collided with a ferry, Turkish media reported.

Fifield reported from Budapest. Souad Mekhennet in Frankfurt, Germany, contributed to this report.

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