While visiting Greece Thursday, EU President Donald Tusk told migrants heading to Europe for economic gains to stay away, as some of the thousands stranded in the north of the country demonstrated to have borders opened further along their route.

"I want to appeal to all potential illegal economic migrants, wherever you are from: Do not come to Europe," Tusk said after meeting Premier Alexis Tsipras in Greece as part of a tour of countries worst affected by Europe's migration crisis.

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

Thousands of migrants are massing at the Greek border to Macedonia as countries along the so-called Balkan route - the main path used by migrants to reach wealthier European countries like Germany and Sweden - have largely been shut down by migration restrictions.

Meanwhile, hundreds of Syrian and Iraqi refugees protesting the closure of the route to Northern Europe blocked a train track near the Macedonian border at the northern Greek village of Idomeni, while 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.

During his visit, Tusk also promised that the European Union would not abandon Greece 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.

"Unilateral decisions without prior coordination, however understandable they are in a national context, are in fact detrimental to the European spirit of solidarity," he said.

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