German Chancellor Angela Merkel says that all EU countries can 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 Ms Merkel had agreed on a mechanism to spread the migrant load across Europe.
But Hungary’s prime minister, Viktor Orban, said he was not prepared to pitch in and questioned how any EU quota system for migrants could work.
Even as calm returned on 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.
Ms 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 Ms 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.
Mr 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,”’ Mr 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 Mr 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 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.
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.