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Recently arrived migrants at the main train station in Munich, Germany, on Sunday.Credit Sven Hoppe/European Pressphoto Agency

BERLIN — With record numbers of migrants pouring across the Hungarian border and rushing west, Germany, the country that had been the most welcoming in Europe, suddenly ordered temporary border restrictions on Sunday that cut off rail travel from Austria and instituted spot checks on cars.

It took the action just one day before European ministers were scheduled to meet in Brussels to discuss a plan to disperse tens of thousands of refugees across Europe, with many governments, particularly in Eastern Europe, bristling at being forced to accept more migrants than they wish to take.

The crisis is the latest, and perhaps thorniest, test of Europe’s willingness to work together to solve big problems amid rising populist, nationalist and Euro-skeptic movements across the continent.

The move by the government of Chancellor Angela Merkel was seen as a strong sign — if not an outright message — to other European Union members that Germany was growing weary of shouldering so much of the burden for Europe’s largest humanitarian crisis in decades without more help and cooperation from other nations.

For others, though, the concern was that if even the richest and most powerful nation in the 28-member union was showing signs of hitting its limit, how would Europe be able to find a path through this seemingly ceaseless refugee emergency?

When word of the new restrictions made the rounds at the main station in Salzburg, Austria, the last major stop on the rail journey to Germany, hundreds of migrants were taken off the blocked trains and to a garage nearby, the German Press Agency said.

A simple sign was posted on the station’s information boards: “No railway service by order of German authorities due to the German migrant crisis.”

Interior Minister Thomas de Mazière said that it was “desperately necessary” for Germany to limit the number of people coming into the country and “reinstate an orderly entry process” after two weeks that left the country straining to accommodate the new arrivals.

European Refugee and Migrant Crisis

Although one of the proudest European achievements of recent decades was passport-free travel between most member nations, the rules allow the reinstatement of border restrictions in cases of crisis and national security, he said.

“This measure is also a signal to Europe” that more needs to be done, and quickly, Mr. de Mazière said. “Introducing temporary border controls will not solve the whole problem,” he said.

Also on Sunday, Ms. Merkel spoke with Jean-Claude Juncker, president of the European Commission, who proposed a plan last week to relocate 160,000 migrants who are bottling up in the main front-line nations of Greece, Italy and Hungary.

The proposal, to be discussed Monday in Brussels by the bloc’s home affairs ministers, includes 40,000 migrants covered under an earlier plan that collapsed when several member nations refused to accept mandatory quotas of refugees, as well as 120,000 more.

Leaders of several countries, including Poland and the Czech Republic, have said they still object to any mandatory quotas, but may be willing to accept more new arrivals as long as it is voluntary.

Hundreds of thousands of migrants and refugees have been surging into Europe for nearly two years from war-torn areas of the Middle East, as well as Afghanistan, Pakistan, Eritrea and elsewhere in Africa. Many of them aim to reach Germany, but others try to get to Sweden, Britain, the Netherlands and other nations.

Previously, the route of choice was across the Mediterranean Sea from Libya. But with that path growing increasingly dangerous, an overland route from Greece to Macedonia to Serbia to southern Hungary started attracting more people this summer.

Hungary’s prime minister, Viktor Orban, responded by beginning the construction of a razor-wire fence along the country’s entire, 108-mile border with Serbia, a project that is still underway.

Mr. Orban also promises a fresh crackdown against those crossing the border when new laws take effect in Hungary on Tuesday, imposing harsh prison penalties for entering the country illegally and allowing the building of “transit centers” right at the border where migrants could be held while their cases were being considered.

In announcing Germany’s new border restrictions, Mr. de Mazière also called for the creation of what he called “waiting zones” along the union’s external borders where migrants could be registered and wait until they were granted refugee status and assigned to a country.

Hungary’s government, which has taken a particularly hard line during the crisis, reacted warmly to Germany’s announcement on Sunday.

“Hungary understands Germany’s decision, and Hungary is standing by Germany,” Peter Szijjarto, the country’s foreign minister, said at a news conference.

He said Hungary welcomed Berlin’s decision, which he described as defending German and European values, adding that Hungary made a new proposal of its own on Sunday: calling for a Continent-wide effort to defend the borders of Greece, the first stop on the migrant path.

The migrants who eventually make their way to Hungary usually begin their journey into Europe with a short, but often perilous, sea crossing from Turkey to one of the nearer Greek islands.

If European leaders could close off that flow, Hungarian officials said Sunday, the numbers moving through the Balkans into Central Europe would dwindle to a trickle. Advocates for refugees say that those determined to reach Europe will only find other paths.

Just how dangerous that sea crossing can be was evident again Sunday when the Greek Coast Guard recovered the bodies of 34 migrants, including 15 children, after their boat capsized in the Aegean Sea. An additional 68 were rescued, and 30 others managed to swim to the nearby island of Farmakonisi.

The land portion of the journey offers dangers, too. The Austrian authorities said they saved 42 people on Sunday from a refrigerated truck near the German border, and arrested two smugglers. Just last month, 71 people were found dead in the back of such a truck near the Austrian-Hungarian border.

Germany has said it expects 800,000 migrants by year’s end, but has indicated up to now that it can handle the newcomers, and even welcomed their addition to its aging work force.

But the numbers arriving have continued to grow, and Germany’s humanitarian network is wobbling under the strain.

On Saturday, around 12,000 migrants arrived in Munich, with 4,000 more by Sunday afternoon. More beds are needed, Munich officials said.

And more migrants are on the way. Before Germany closed off rail traffic from Austria, Austrian officials said 500 migrants were arriving every hour at the main border crossing between Hungary and Austria, with 7,000 crossing that day before 3 p.m.

On the Serbian border, the Hungarian authorities said that 4,330 migrants were detained Saturday for crossing illegally, an increase of 700 over the previous one-day record. And many thousands more are waiting to cross behind them, or making their slow way to the border.

“The influx is simply not stopping right now,” said Lt. Col. Helmut Marban, a police spokesman in Austria’s easternmost state. “We really have our plates full.”

Guntram B. Wolff, director of Breugel, a Brussels research group, said Germany’s decision to impose controls seemed to be “an interim thing,” rather than a sign that the European Union, panicked by a disorderly influx of migrants, was retreating from the principle of open borders.

“It is just a measure to slow down the flow and to handle things in a more orderly manner,” he said.

But if some Europe-wide agreement is not reached to deal with the crisis, Mr. Wolff said, the so-called Schengen system that allows passport-free travel across 26 countries is in danger of collapsing.

“There has to be a European solution, and if there is not one, then Schengen will come under pressure,” he said. “For the moment, Schengen is still there.”

Abdelkahar Sherzad, a 28-year-old from Afghanistan, heard about Germany’s new restrictions only after waiting four days for a train out of Budapest’s Keleti station.

“I would really like to go to Germany,” Mr. Sherzad said. “But if they don’t let me go, I will consider other options, like staying in Austria or trying to go to another country. I won’t stop.”