A column of thousands of people fleeing war and poverty made it to Western Europe on Saturday, after forcing Hungary’s anti-
immigrant leaders to yield in a days-long campaign to turn them back. But with a fresh rush of migrants at Europe’s borders, the broader refugee crisis only looked to be worsening.

The Hungarian reversal was a defeat for the country’s nationalist prime minister, Viktor Orban, who had declared himself a defender of Europe’s Christian heritage against the mostly Muslim families seeking entrance. He has vowed to seal the country’s southern border by Sept. 15. But with passage to Europe soon to grow more difficult, the number of newcomers has only expanded in the continent’s worst refugee crisis since the Balkan wars of the 1990s.

New asylum-seekers were arriving in Hungary as quickly as they were draining out Saturday, highlighting the absence of a unified European plan for their accommodation. Germany and Sweden have thrown open their doors to people fleeing Syria’s war. Other nations have barred themselves shut.

The turnabout began in the early hours of Saturday, when Hungary’s leaders dispatched blue city buses to pick up migrants who had paralyzed traffic when they set off on the hundred-mile trek to Austria after spending days in squalid conditions in Budapest. By midday, the asylum-seekers were limping across the border into the arms of Austrian volunteers. As the day ended, thousands were pulling up on trains in Germany, where they were receiving sustenance, shelter and welcome in a nation that has declared no limit to the numbers it will aid. As many as 7,000 were expected Saturday.

“I had a smile to both my ears. I was finished with Hungary,” said Omar Mansour, a 24-year-old Syrian physical education teacher, who sat Saturday on a large stone in the border-station parking lot in the pastoral Austrian town of Nickelsdorf, warming himself against the September chill with a green sleeping bag before he continued on to Germany. He said he had spent the past week at Budapest’s main train station, where a makeshift refugee camp accumulated after authorities blocked migrants’ paths to Western Europe on Tuesday.

Fresh asylum-seekers continued to arrive at Hungary’s southern border — more than 2,500 since the beginning of Friday, according to Hungarian border police. In a change of policy, the newcomers were being allowed to take local trains to the Austrian border. Budapest’s Keleti railway station, which over the course of the week had become packed with tents, crying children and anxious refugees, reverted to a place where purposeful asylum-seekers bought tickets to travel onward.

Reminders of World War II

But there remained no European plan in place to handle the torrent of human need, despite the continent’s pride in having moved past its World War II-era horrors to build some of the most prosperous societies in the world.

Instead, the week’s images reverberated uncomfortably with some of the worst memories of that period. Hungarian authorities tricked migrants into getting onto trains in a bid to speed them to detention camps where they would be held and processed, an effort that had shadows of Nazi-era deportations. Czech authorities wrote tracking numbers directly onto refugees’ arms, in a gambit to keep them organized that bore an unfortunate resemblance to concentration camp tattoos.

“All of Europe needs to wake up,” said Austrian Interior Minister Johanna Mikl-Leitner. “In this great challenge, the continent needs to give an answer,” she said on a day when E.U. foreign ministers met in Luxembourg to discuss the crisis but came away as divided as ever about how to handle it.

The U.N. refugee agency has said that Europe needs to create as many as 200,000 spots for new refugees. Plans circulating in Brussels appear far less generous.

Many countries are reluctant to take in any refugees at all. Slovakia wants only Christians.

The absence of an agreement has led individual nations to take radically different approaches to the problem. Hungary has built a 108-mile fence of razor wire at its border with Serbia, and leaders have vowed to deploy the army to keep new migrants from entering. Sweden, meanwhile, is offering permanent residency to Syrian refugees.

Orban had painted his hard-line approach to the mostly Muslim asylum-seekers as a stand to preserve Europe as a Christian continent.

“The supply of immigrants is endless,” he told his ruling party’s annual picnic on Saturday. “If everyone is admitted, it will destroy Europe.”

Orban and British Prime Minister David Cameron have criticized the German open-door approach for spurring a vast flow of asylum-seekers to Europe, many of whom have taken dangerous routes to get there. Cameron has said that the solution to the crisis lies in achieving peace in Syria, not in taking in more refugees.

German Chancellor Angela Merkel and her allies have countered that Europe has a humanitarian duty to help people fleeing war and that the bloc of 503 million people is wealthy enough to bear the costs if it is done in an equitable fashion. She and her allies have called for mandatory quotas to spread the burden across Europe.

German officials have said they expect to take in as many as 800,000 asylum-seekers this year.

“The right to political asylum does not have a limit on the number of asylum-seekers,” Merkel said Saturday. “As a strong, economically healthy country, we have the strength to do what is necessary,” she told the Funke media consortium.

At the border crossing between Hungary and Austria, people handing out aid were shocked by the experiences of the arriving migrants. There was such a large flood of asylum-seekers being received on the Austrian side that authorities there shut down traffic for hours, sending a miles-long backup into Hungary.

“It feels like a little war here,” said Andreas Zenker, a spokesman for the Austrian Red Cross who was distributing aid Saturday at the Austrian border. “They came in, and they were injured. Small children with barely any food. It’s crazy.”

Nour al-Qattan, a 29-year-old accountant from Damascus, said she had walked along the highway for more than 10 hours before Hungarian buses pulled up early Saturday.

“I had doubts, because I thought they would take us to a camp in Hungary. I thought it was a trick,” she said as she waited to be taken farther into Western Europe.

E.U. refugee rules have proved inadequate for the crisis because they place most of the burden of dealing with asylum-seekers on the first E.U. country they enter. That has forced poorer countries such as Greece, Hungary and Italy to the forefront as richer ones have taken a back seat.

Headed onward

For now, the crisis appears likely to continue unabated. At Budapest’s fin-de-siecle train station Saturday, many asylum-seekers were matter-of-factly moving on to Western Europe.

“At 8 o’clock we will get a train to Germany. Then we will go to Finland or Belgium to live,” said Reham Ahmed, 15, who arrived with her family in Budapest on Saturday — after all the drama of the past week — and who said they were simply passing through on the way to a better life.

Birnbaum reported from Brussels. Stephanie Kirchner in Berlin and Andras Petho in Nickelsdorf contributed to this report.

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