Refugees from the Middle East are silhouetted against the setting sun as they walk on railway tracks in Roszke, Hungary, on Sunday. (Darko Bandic/AP)

European leaders traded barbs Monday about who was to blame for a worsening migration crisis, as mounting calls to take in desperate asylum-seekers mixed with skepticism that swift changes would actually take place.

There was little unity ahead of an emergency meeting planned to be held in two weeks, despite a growing agreement that Europe’s unpredictable asylum system has spurred migrants to take dangerous steps to scale the continent’s high walls. The problem has grown worse by the day, with aid groups in Greece saying that new arrivals were on track Monday to top record-breaking weekend highs.

From Greece, migrants flow northward through the Balkans in an attempt to reach Western Europe, where generous benefits can await. But if they are caught by poorer E.U. countries along the way, their future can be grim, a disparity that has spurred many to pay smugglers to sneak them into the heart of Europe. That gamble can have tragic consequences. Last week, the bodies of 71 presumed migrants were found in the back of a delivery truck on an Austrian roadside. They are thought to have suffocated,

At a time when Germany is taking the lion’s share of refugees — an estimated 800,000 this year alone — Chancellor Angela Merkel on Monday urged other nations in the European Union to share the burden. She called for new E.U.-run asylum processing centers in entry nations such as Greece to better assess and safely funnel refugees deeper into Europe.

“There’s no point in publicly calling each other names, but we must simply say that the current situation is not satisfactory,” Merkel told reporters in Berlin, saying the system needed urgent change.

Top E.U. officials plan to meet Sept. 14 to try to streamline the fragmented asylum process.

The leaders of Germany and France want to achieve that goal by speeding deportations of economic migrants while allocating more resources to people fleeing the wars in Syria, Iraq and elsewhere. They have also proposed a quota system under which each of the 28 E.U. nations commits to resettle a certain number of refugees, taking aim at countries such as Hungary, which is building a fence to keep migrants out.

“Our responsibility is to make sure that asylum rights are respected,” French Prime Minister Manuel Valls said Monday during a visit to the French port city of Calais, where migrants seeking to reach Britain have gathered. “To do so, we cannot build barbed-wire fences against those who are tortured in their own countries.”

But there were signs that unity within Europe’s consensus-driven policymaking would be elusive. Slovakian Prime Minister Robert Fico on Monday firmly rejected any decision that would force his nation to take in a fixed number of refugees.

“We strongly reject any quotas,” Fico told reporters in the Slovakian capital, Bratislava, according to the news agency Reuters. “We will wake up one day and have 100,000 people from the Arab world, and that is a problem I would not like Slovakia to have.”

Britain, too, seems unlikely to throw open its doors. Over the weekend, British Home Secretary Theresa May said she wanted to cut back even legal migration from other E.U. nations.

The patchwork of responses in Europe appears to be fueling a booming trade for smugglers, who help migrants get from less-generous nations such as Hungary into Germany, which awards far more benefits to refugees.

Migrants are under pressure because of the wide disparities in the way European countries have responded to the crisis. A quirk of European law allows nations to deport asylum-seekers to the first E.U. country where their presence was registered by authorities.

Hungary’s far-right leaders have had the toughest response in Europe, stringing a line of razor wire along their country’s 109-mile border with Serbia and building a taller fence behind it.

Crowds of asylum-seekers packed Budapest’s fin-de-siecle train station on Monday. There were signs that Hungarian authorities were relaxing their hard-line stance, allowing hundreds of migrants onto trains headed to Austria, from where many planned to continue on to Germany.

The unpredictable policies have fueled many migrants’ willingness to pay as much as several thousand euros to smugglers who move them to their destinations out of sight from authorities.

E.U. leaders have grown increasingly concerned about the problem.

“The only people who benefit from unilateralism are the smugglers,” said Alexander Betts, director of the Refugee Studies Center at the University of Oxford. “About the only area where there’s consensus in Europe is that the current system is dysfunctional.”

Separately, Greece’s coast guard said Monday that it had picked up more than 2,400 migrants in dozens of sea-based search-and-rescue missions over the weekend, a sign that the flow of asylum-seekers is continuing unabated.

Aid workers on the Greek island of Lesvos, a first port of call for many migrants coming from Turkey, which neighbors Syria, said it was swiftly becoming overwhelmed with new asylum-seekers, who are arriving faster than others can be transported away.

“The system broke this weekend, particularly yesterday,” said Simon Clarke, deputy team leader of the International Rescue Committee team on Lesvos. In a telephone interview, he said Monday’s numbers appeared likely to rival the about 4,000 who arrived a day earlier — nearly four times as many as had been coming just 10 days ago.

Refugee advocates also want to establish a process by which asylum-seekers could file applications with Europe even before they cross the continent’s borders. Armed with the proper paperwork, they could bypass the dangerous sea journey altogether.

But even the most generous E.U. nations may be wary of creating too streamlined a process for refugee claims, fearful that they would make it too easy for the millions of Syrians who have fled to Turkey, Lebanon and Jordan to move to Europe, analysts say.

“It’s not the fear of who comes this year, but of how many could come next year, and the unknown, that sometimes holds politicians back from establishing a process that would help countries like Turkey and Lebanon,” said Elizabeth Collett, director of the Migration Policy Institute Europe.

Faiola reported from Berlin. Stephanie Kirchner in Berlin contributed to this report.

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