BRUSSELS (AP) — The European Union's top migration official told Austria Tuesday that its plan to cap the number of people who can apply for asylum is unlawful, but Austrian Chancellor Werner Faymann refused to back down.

As EU leaders sought to end their fragmented response to Europe's biggest refugee emergency since World War II at a summit meeting, the legal fight with EU Migration Commissioner Dimitris Avramopoulos took center stage.

"Legal opinions will be answered by lawyers. Politically I say: we'll stick to it," Faymann said as he arrived at the summit in Brussels.

More than 1 million people entered the EU in 2015 fleeing conflict or poverty, and some 84,000 have entered so far this year. Overwhelmed by the numbers and frustrated by their inability to agree on an effective European response, some EU countries have begun tightening border controls or putting up fences without warning their neighbors.

In the latest in a series of uncoordinated and unilateral measures by nations, Austria announced on Wednesday that it would allow no more than 80 people a day to apply for asylum at its southern border points, as of Friday.

But Avramopoulos said in a letter Thursday that "Austria has a legal obligation to accept any asylum application that is made on its territory or at its border."

The letter to Austrian Interior Minister Johanna Mikl-Leitner, seen by The Associated Press, said a ceiling on asylum-seekers "would be plainly incompatible with Austria's obligations" under EU and international law.

Mikl-Leitner has said that a maximum 3,200 people a day would be allowed to enter Austria "who are seeking international protection in a neighboring country." That is an allusion to Germany which, along with Sweden, has been the preferred destination for most migrants.

But Avramopoulos also warned that Austria should not be allowing people to travel through the country if their aim is to apply for asylum elsewhere.

European Parliament President Martin Schulz told the leaders that "the problem is that everyone sees the situation from their individual standpoint and waits for the other to move first in implementing those necessary solutions,"

"Lamentably, this crisis is exposing serious fault-lines within our union," Schulz said.

Dutch Prime Minister Mark Rutte said he understood the reaction of countries like Austria, but he warned that the end result could be "the bunching up of great amounts of people in difficult circumstances in northern Greece."

Greece has been overwhelmed by the entry of some 850,000 people last year, mostly from Turkey. Thousands are still entering every week. The Greek coastguard has been swamped, and the country has barely 10,000 places to shelter those arriving.

The EU's executive Commission has given Greece three months to restore order on its borders, but few believe Athens will be able to meet the deadline. The Commission fears that countries on the main migrant route north are working to close Macedonia's border with Greece.

"If Greece and Turkey do not dramatically decrease the number of migrants coming to EU in next few weeks, then talk about closing the borders of Central Europe and securing the borders of Western Balkans will become a new reality," warned Czech Prime Minister Bohuslav Sobotka.

But Greek Prime Minister Alexis Tsipras appealed for the EU to "remain united and show solidarity."

"Europe cannot be rules for some and al la carte for others," he said.

The leaders are also looking at ways to keep up pressure on Turkey to deliver its pledge to crack down on migrants trying to cross into Greece.

The EU has offered Ankara 3 billion euros for the more than 2 million Syrian refugees on its territory, as well as easing visa rules for Turks and the fast-tracking of its EU membership process.

"It is good if Europe and Turkey share the burden, but we need clearer protection of the external borders, we need a fight against smugglers and illegality — we have to find legal ways for people to come to the European Union," German Chancellor Angela Merkel said.

Raf Casert in Brussels and Geir Moulson in Berlin contributed to this report.