German Chancellor Angela Merkel, reflecting on "a moving, in some parts breathtaking weekend behind us," said Monday that all EU countries could help to accommodate the human tide from the Middle East and Africa.
French President Francois Hollande announced that his country would welcome 24,000 refugees, and that he and Merkel had agreed on a mechanism to spread the migrant load across Europe.
But Hungary's prime minister, Viktor Orban, said he wasn't prepared to pitch in and questioned how any EU quota system for migrants could work.
Even as calm returned Monday to the main border point between Austria and Hungary after more than 14,000 people used it over the weekend to enter Austria, Hungary's leader hit back at EU counterparts who blamed his country for the chaos.
Merkel told reporters in Berlin that Germany will ensure that those who need protection receive it, but that those who stand no chance of getting asylum will have to return to their homes swiftly. Germany is preparing to receive by far the largest number of immigrants, but Merkel called for help from EU partners.
"Germany is a country willing to take people in, but refugees can be received in all countries of the European Union in such a way that they can find refuge from civil war and from persecution," she said.
Orban mocked the European Union's efforts to distribute migrants through a quota system and compared Hungary to a "black sheep" representing a voice of reason in the EU flock of countries.
Any EU migrant quota among the bloc's 28 countries, makes no sense in a system where the free movement of people would make it impossible to enforce, he said.
"We represent the position of what the Americans call 'first things first,'" Orban told Hungarian ambassadors meeting in Budapest. "As long as we are unable to defend Europe's external borders, it makes no sense to talk about the fate of the immigrants."
Austria's Chancellor Werner and other EU leaders have blamed Orban for the chaos they say left Austria and Germany no choice but to essentially open their borders for thousands of migrants and refugees who complained of neglect and human rights violations in Hungary.
Most of those crossing into Austria over the weekend proceeded by train to Germany. Austrian officials said only about 90 people asked for asylum in Austria.
Further south tensions were high Monday in Macedonia at the border with Greece, where scuffles broke out between police and thousands of people attempting to head north toward the European Union.
About 2,000 people had gathered at the Greek border near the village of Idomeni just after dawn, attempting to cross into Macedonia. But Macedonian authorities were allowing only small groups to cross every half hour, leading to tension. The situation later calmed after more were allowed to cross, with about 1,000 having passed the border by mid-day.
Greek police said about 5,000 people had crossed the border heading north in the 24 hours from Sunday morning to Monday morning.
Greece's migration minister estimated that at least two-thirds of the 15,000-18,000 refugees and economic migrants stranded in "miserable" conditions on the eastern Aegean island of Lesbos will be ferried to the mainland in the next five days. Lesbos bears the brunt of the refugee influx, with more than 1,000 arriving daily on frail boats from nearby Turkey.
In a late night meeting that lasted until early Monday in Berlin, the German government agreed to spend 6 billion euros ($6.6 billion) next year to support the hundreds of thousands of new arrivals. At the same time, it also agreed to introduce legal measures making it easier to deport-asylum seekers from countries considered "secure states" like Montenegro, Kosovo and Albania. Asylum-seekers will also get less cash in the future and more non-cash benefits.
German officials recently predicted that up to 800,000 migrants will arrive by the end of the year, many of them refugees fleeing war and persecution in Syria, Iraq and Eritrea.
The government's aid package will include improved housing, more federal police and language classes.
Merkel's deputy, Sigmar Gabriel, said integrating the migrants into German society would require confronting the fears of the country's native population.
"I say this quite openly, there will be conflicts," the economy minister told reporters. "The more openly we talk about the fact that people are worried, that there's fear in the country and that there may be conflicts, will I think help us deal with this realistically and confront reality."
Five asylum seekers were injured in a fire early Monday in Rottenburg in southwest Germany, the German news agency dpa reported. Three of them were injured when they jumped out of the burning building, while two others had to be treated for smoke inhalation. The cause of the fire was not immediately clear.
Austrian police spokesman Helmut Marban said that no migrants had arrived at the Nickelsdorf border point since before midnight, when 260 people crossed into Austria and left shortly afterward by train to Vienna.
Beyond the Red Cross tent set up near the crossing and the stores of food, empty cots set up in a parking lot, hygiene articles and other goods stacked up for any new arrivals, there was little to indicate Monday morning that the border had served over the weekend for the dramatic influx of Syrians, Iraqis, Afghans and others.
An AP reporter counted about five vehicles driving into Austria over two minutes, and slightly fewer in the other direction. The truck lane, which was backed up on the Austrian side after being blocked off over the weekend, was empty.
Jahn reported from Vienna. Pablo Gorondi in Budapest, Lori Hinnant in Paris, Kirsten Grieshaber in Berlin and Giannis Papanikos in Idomeni, Greece, contributed to this report.