Bitterly-divided European leaders will seek to find a credible response to the continent's worst migration crisis since World War Two at an emergency summit this week.
German chancellor Angela Merkel called on her peers on Sunday to accept joint responsibility.
"Germany is willing to help. But it is not just a German challenge, but one for all ofEurope," Merkel told a gathering of trade unionists. "Europe must act together and take on responsibility. Germany can't shoulder this task alone."
Striking a more sceptical tone on migration than in previous weeks, Merkel also warned that Germany could not shelter those who were moving for economic reasons rather than to flee war or persecution.
"We are a big country. We are a strong country. But to make out as if we alone can solve all the social problems of the world would not be realistic," she told a gathering of the Verdi trade union.
European Council President Donald Tusk, who chairs European Union summits, said on Twitter on Sunday following a weekend visit to Jordan and Egypt that the EU needed to help Syrian refugees find a better life closer at home.
That will be one of the topics of discussion for Wednesday's summit in Brussels as hundreds of thousands of refugees and migrants brave the seas and trek across the impoverished Balkan peninsula to reach more affluent countries in northern Europe.
The 28-member bloc has struggled to find a unified response to the crisis, which has tested many of its newer members in the East that are unaccustomed to large-scale immigration.
On Sunday Hungary erected a steel gate and fence posts at a border crossing with Croatia, the EU's newest member state. Overwhelmed by an influx of some 25,000 migrants this week, Croatia has been sending them north by bus and train to Hungary, which has waved them on to Austria.
Around 10,700 migrants walked into Austria from Hungary on Sunday, some 200 more than on Saturday.
The influx of migrants, most of them fleeing war and poverty in the Middle East, Africa and Asia, has led to bitter recriminations between European governments while the temporary closure of national borders has undermined one of the most tangible achievements of the Union.
"If you don't cope with this crisis, then I think the EU will fall apart," said a senior EU official.
The official said European leaders would discuss longer-term strategies for dealing with the crisis, particularly increasing cooperation with Turkey and the countries bordering Syria to keep the millions of refugees at home. Tusk said more aid to the World Food Programme and the United Nations High Commissioner for Refugees would also be on the agenda.
Beefing up the EU's asylum agency, Frontex, into a full border and coastguard agency, and working on hotspots and a list of "safe countries" whose citizens would not normally qualify for asylum, would also be up for discussion, the official said.
On Saturday, German Vice-Chancellor Sigmar Gabriel said the EU needed to provide 1.5 billion euros ($1.70 billion) to the two agencies to address funding shortfalls.
The EU prides itself on cementing peace among countries that until World War Two fought bloody battles and fostering prosperity by removing internal barriers among its member states through the so-called Schengen agreement.
But the more than 500,000 people crossing the Mediterranean into Europe this year alone and Hungary's use of water cannon and razor wire on its border with Serbia have seen the EU's ambitions to act as one fall short.
The picture of a dead toddler washed up on a beach in Turkey sent shockwaves around the continent. On Sunday 13 migrants, including six children, were killed as their boat was wrecked in Turkish waters.
"The (Schengen) agreements are now part of our daily lives and it is unthinkable that the facilities enjoyed by hundreds of thousands of travellers and cross-border workers in Europe are challenged by nationalist and reactionary thoughts and political actions," said Jean Asselborn, Minister of Foreign and European Affairs for Luxembourg.
As the holder of the rotating presidency of the EU, Luxembourg is working to broker a compromise that can break the deadlock between member states on sharing the burden of the crisis.
EU interior ministers, meeting on Tuesday, are expected to agree on a voluntary relocation scheme to redistribute 160,000 refugees from frontline states across the EU, a fraction of the total entering Europe.
French President Francois Hollande said he wanted the interior ministers to address the most difficult aspects of the migration crisis by Tuesday so that EU leaders could focus exclusively on financing at Wednesday's summit.
"I really wish all these issues to be solved by the ministers' reunion," Hollande said on Sunday during a state visit toMorocco.
EU ambassadors met on Sunday to try to hammer out compromises ahead of Tuesday's meeting but several issues still needed to be solved and work would continue until then, said a spokeswoman for the EU presidency.
Germany's Gabriel warned that the country could be overwhelmed by the 800,000 refugees and asylum seekers it expects to receive this year. Most of the migrants hope to reach prosperous Germany or Sweden.
U.S. Secretary of State John Kerry said on Sunday the United States would take in 15,000 more refugees from around the world next year, increasing the current level to 85,000, and to 100,000 in 2017.