Top EU officials on Thursday warned economic migrants to stay away from Europe and those qualifying for asylum to not expect a choice on which country they can settle in, as tensions continued to mount in migrant-clogged Greece.

Europe has struggled to get under control migrant flows that stretch from Turkey to Greece and through the Western Balkans to wealthy northern European countries such as Germany or Sweden.

More than 1 million people reached European shores last year. Many were fleeing conflicts in the Middle East and have the right to apply for asylum in the European Union. But economic migrants who do not qualify for international protection have also joined their ranks.

Thousands of people have now started massing at the Greek border to Macedonia, as countries further north along the Balkan migration route have started restricting passage through their territories.

Hundreds of Syrian and Iraqi refugees protesting the closure of the route blocked a train track on Thursday at the northern Greek village of Idomeni, chanting "open the border."

Officials estimate that 12,000 to 15,000 people needing urgent humanitarian assistance are in the area around Idomeni, waiting for permission to continue their journey. But Macedonian authorities are letting through fewer than a couple of hundred a day.

As many as 70,000 people could be stranded at the border by the end of the month, Greek officials have said.

EU President Donald Tusk, who will chair a special EU summit on migration in Brussels next week, visited Greece on Thursday as part of a tour of countries worst affected by the migration crisis.

"I want to appeal to all potential illegal economic migrants, wherever you are from: Do not come to Europe," Tusk said in Athens.

"Do not believe the smugglers. Do not risk your lives and your money. It is all for nothing," he added, warning that migrants will no longer be simply waved through from country to country.

In The Hague, meanwhile, the president of the European Commission warned that asylum seekers cannot all expect to go to northern Europe.

"What really disturbs me - and we see this every day - is that refugees ... just decide themselves where they want to go. All the refugees in Greece say 'Germany, Germany, Germany,' and that cannot be," Jean-Claude Juncker said in a speech.

"I also get tears in my eyes when I see the current pictures, but you have to know that the situation is not black and white. Governments have to do more, but the refugees have to also be ready to cooperate," he added.

During his visit in Greece, Tusk promised that the EU will not abandon the country and its people, which he said are "paying a very high price for a problem they themselves did not create."

Tusk has been trying to convince countries affected by migration to join forces in a European response to the crisis, rather than acting unilaterally and undermining the "European spirit of solidarity."

Greek Prime Minister Alexis Tsipras said he would demand at Monday's summit that sanctions be brought against those EU countries which are not implementing decisions taken by the bloc.

Turkey will also be participating in the Brussels summit. Tusk started a two-day visit to that country on Thursday afternoon by meeting Prime Minister Ahmet Davutoglu. Talks with President Recep Tayyip Erdogan are due to follow Friday.

"The EU appreciates our good and growing cooperation with Turkey to prevent irregular migration," Tusk said in Ankara. "At the same time, we agree that the refugee flows still remain far too high and that further action is needed."

Also on Friday, the commission will present a report on how to "return order to the management of the EU's external and internal borders," spokesman Margaritis Schinas said.

A draft of the report seen by dpa lays out a roadmap for "a return to a normally functioning Schengen" - Europe's much-cherished free movement area - by November, including by having a new European border and coast guard "start functioning during the summer."

"If we do not better protect the [Schengen] external borders, especially the one between Greece and Turkey, then we will never reign in this crisis," Juncker said.

The uncontrolled migration flows have led several countries in Schengen to reestablish border controls, which are also having an economic impact.

The commission's draft report pointed to estimates that "reintroducing internal border controls on a systematic and long term basis could cost between up to 5 billion euros (5.5 billion dollars) and up to 18 billion euros in overall direct costs alone."

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