EU President Donald Tusk on Thursday warned economic migrants not to come to Europe, as he castigated member states for taking unilateral action to tackle the crisis.

"I want to appeal to all potential illegal economic migrants wherever you are from: Do not come to Europe," Tusk told a press conference in Athens after talks on the refugee crisis with Greek Prime Minister Alexis Tsipras.

"Do not believe the smugglers. Do not risk your lives and your money. It is all for nothing."

To Tsipras' delight, Tusk then attacked one-sided actions by EU states that "erode trust" by dividing the bloc as it faces its greatest migration challenge since World War II.

"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.

The comments were an apparent reference to Austria's move to restrict passage to migrants, leading to a domino effect further down the migrant trail as Slovenia, Croatia and non-EU members Macedonia and Serbia followed suit.

The clampdowns have left Greece with a huge bottleneck of migrants stuck on the border with Macedonia as authorities there let only a trickle through, with the EU estimating the number stranded could be as high as 12,000.

Hungary, Poland, Slovakia and the Czech Republic have also vowed to help Bulgaria and Macedonia seal their borders with Greece, should Athens fail to stem the tide of migrants arriving from Turkey by mid-March.

Tsipras on Thursday said he would like to see sanctions imposed on EU states that undermine joint decisions by the bloc.

"Greece will demand...that there be sanctions to those who do not respect (European solidarity treaties)," the Greek premier said.

"What is agreed must be respected."

EU hardliners have called for Greece's expulsion from the bloc's passport-free Schengen zone unless it takes stronger action to stop the migration flow.

But Tusk on Thursday said this was no solution to the crisis.

"Excluding Greece from Schengen is neither an end nor a means in this crisis. Greece is part of Schengen, of the euro area and of the European Union and will remain so," he said.

"Greece or any other European country will no longer be a transit country. The Schengen rules will enter into force again."

Tusk was in Athens as part of a regional tour on the migration crisis that has also seen him travel to Slovenia.

He will meet Turkish Prime Minister Ahmet Davutoglu later Thursday in Ankara, where he will urge Turkey to offer more "intensive" help in reducing the flow of migrants to Europe.

Tusk will then travel on to Istanbul for talks on Friday with President Recep Tayyip Erdogan ahead of next week's EU summit with Turkey in Brussels, where the migrant crisis will top the agenda.