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Migrants on Monday at the Schwarzlsee reception camp in Graz, Austria, where they receive food, shelter and health care before they move on to Germany.Credit Sergey Ponomarev for The New York Times

NICKELSDORF, Austria — In the absence of a unified plan by the European Union, consistent national policies or any consensus on the best way to end the worst humanitarian crisis on the Continent since World War II, Austria is stepping up to house thousands of migrants from the Middle East and Asia, fast becoming Europe’s distribution center of people seeking safety and a better life.

Austria, a nation of 8.7 million, has been assembling Syrian refugees and others who have reached its border after a treacherous journey across the more hostile Balkan states, feeding and housing them and providing health care before routing them toward Germany.

In imposing some order on the human flow, Austria has served as a safety valve for countries to the south and a regulator for the stream of migrants who would otherwise pour into Germany, which is straining to keep up.

Since the start of the weekend, reception centers and other camps had received more than 26,000 people — 10,500 on Saturday, 10,700 on Sunday and 5,000 on Monday, all from Hungary. Most of the 2,700 migrants who massed on Slovenia’s southern border with Croatia in the past few days had passed through and onto Austria, officials said.

On the other side of the country, in Salzburg near the border with Germany, the authorities were expecting about 1,000 people on Monday from camps inside Austria. There, some have been put quietly on trains and sent to reception centers in Germany for processing and distribution throughout its states.

The operation is in stark contrast to the greater European response, in which leaders appear to be making little progress on a policy that will share responsibility for the migrants among the 28 European Union member states.

The foreign ministers of the Czech Republic, Hungary, Poland and Slovakia met in Prague on Monday, in advance of an emergency meeting of union leaders on Wednesday in Brussels.

The Eastern European ministers did not issue a formal statement, but their governments have made it clear that they will not accept a European Union plan spearheaded by Germany to require the members of the bloc to take in migrants according to a formula based on wealth and population.

“The real solution would be the E.U. regaining control over its own borders,” said Foreign Minister Peter Szijjarto of Hungary. “The quota system is unenforceable. The conditions for its implementation are not there.”

He accused Greece and Croatia, two members of the European Union, of violating European law: Greece by failing to prevent an influx of migrants, and Croatia by flooding Hungary and Slovenia while failing to register them.

European Refugee and Migrant Crisis

Under what are known as the Dublin Regulations, people who seek asylum in the European Union are required to register and apply in the member country where they first set foot.

Croatia blamed Greece for the crisis. “It is absolutely unacceptable to have Greece emptying its refugee camps and sending people towards Croatia via Macedonia and Serbia,” said the Croatian interior minister, Ranko Ostojic.

On Monday, Hungary’s Parliament approved rules giving more powers to the army to enforce the country’s borders with Serbia, Croatia and Slovenia. Last week, Hungary adopted legislation making illegal border entry a crime, subject to imprisonment and expulsion.

As the United Nations prepared to convene its annual meeting, Secretary General Ban Ki-moon issued a statement calling on European leaders to show leadership and compassion.

Anthony Lake, the executive director of Unicef, the United Nations Children’s Fund, told reporters at a briefing in New York that his agency had been working over the last few weeks “to considerably ramp up what we’re doing” to serve migrant children traveling into European countries. But he also expressed worry about his agency’s limited budget and fear of compromising Unicef’s Syrian refugee work in the Middle East.

“One of our concerns is precisely that we don’t rob the Peter of the countries surrounding Syria to pay the Paul of Europe,” Mr. Lake said. 

E.U. Official Says ‘Europe in Bad Shape’

The United States announced Monday that it would provide an additional $419 million in humanitarian aid for emergency health care, safe drinking water, food, shelter and other relief supplies to Syrians affected by the civil war there. The money will be distributed to organizations, including Unicef, aiding Syrians still in Syria and those in Lebanon, Turkey and elsewhere in the region. The White House said that would bring the total American commitment to the refugee crisis to $4.5 billion.

In Austria, many migrants said they were stunned at their treatment after journeys through nations to the south and east where officials were only too happy to simply push them north.

“This is unbelievable. I am so happy,” said Zuhair, 23, a chemistry student from Homs, Syria, who did not want to give his last name because of fears for relatives he left behind. Less than a month ago, his hometown was “pure hell,” he said, as “people around me were dying every single day.”

The process is smooth. On Monday, a train carrying 1,800 migrants arrived late in the afternoon on the Hungarian side near Nickelsdorf. The people walking across the border brought the total of new arrivals to 5,000 since that morning, said Helmut Marban, a spokesman for the Burgenland police.

From the border station at Hegyeshalom in Hungary, migrants crossed a grassy field on the frontier between Hungary and Austria. As they approached, Austrian police officers greeted them with a cheerful “Hallo, Österreich,” drawing looks of relief.

“Austria is very good, nice,” said Mohamed Hoseini, 44, from Damascus. He said he had spent 14 hours in a Hungarian train with no food or water.

On Slovenia’s northwestern border, a center into which people had been bused from the Croatian border the night before emptied out just after lunch. All 387 migrants, impatient with the Slovenian authorities’ slow pace in moving them along, simply walked several hundred yards into Austria.

In the central Slovenian city of Celje, about 150 people, most of them Syrian refugees, left a center set up in a high school, bought tickets at the railway station and boarded a train to Vienna.

“We didn’t want to spend another night in the camp,” Merhin, 20, an engineering student from Aleppo, said. “We are extremely happy now.”