Ankara (AFP) - EU President Donald Tusk on Thursday issued a blunt warning to economic migrants not to come to Europe, and chastised European countries which have taken unilateral action to tackle the crisis.

On a busy day of diplomacy, Tusk visited Greece and Turkey, the two countries on the frontline of Europe's worst migration crisis since World War II, and acknowledged that the number of people seeking to reach EU territory from Turkey remained "far too high".

His travels were aimed at building momentum ahead of a critical summit between EU and Turkish leaders on Monday at which Brussels hopes to take concrete decisions leading to a lasting reduction in the flow of migrants and refugees fleeing war, poverty and persecution.

After talks in Athens with Greek Prime Minister Alexis Tsipras, Tusk told economic migrants it was pointless to try to reach the European Union, which is struggling because of the migrant crisis to maintain its prized Schengen passport-free travel area.

The EU plans to unveil on Friday a "roadmap" to restore Schengen -- a keystone to the spirit of European unity.

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

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

In Ankara, Tusk sought to encourage Turkey to take further action to sharply cut the numbers of people taking to unseaworthy boats to reach Greece.

"It is for Turkey to decide how best to achieve such a reduction," Tusk said after meeting Prime Minister Ahmet Davutoglu, floating the idea of a "fast and large scale mechanism" to ship back irregular migrants from Greece.

"It would effectively break the business model of smugglers."

- 'I will try' -

The crisis has raised fears for the Schengen zone as more states bring back border controls, with both Sweden and Denmark announcing another temporary extension of border identification checks on Thursday.

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But sources in Brussels said the EU's "roadmap" on Friday would outline a plan to restore the Schengen zone to full force by November.

The plan, a draft of which has been seen by AFP, includes quickly creating an EU coastguard system and strengthening Greece's external borders.

At the Greek-Macedonian border, migrants from countries like Egypt and Pakistan -- and therefore not classed as refugees -- remained undeterred, despite the many hurdles.

"I know the border is closed but I want to go to Germany, I will try, try, try," said Mohamed, an Egyptian who plans to pay smugglers to sneak into Macedonia through the hills.

"Egypt is bad, there is no work."

According to the International Organization for Migration, 120,369 migrants arrived in Greece from Turkey so far this year. At least 321 died en route.

With thousands stuck on the Greek-Macedonian border after Austria and Balkan states began tightly restricting migrant entries, Tusk lashed out in Athens at "unilateral" actions by EU members as "detrimental to the European spirit of solidarity".

Tsipras said he would like to see sanctions imposed on EU states that undermine joint decisions by the 28-member bloc.

His Deputy Defence Minister Dimitres Vitsas said there were now nearly 32,000 migrants on the Greek islands and the mainland, and a senior UN migration official said the number could surge to 70,000 in the coming weeks.

- 'Looming emergency' -

On Wednesday, the EU unveiled a 700-million-euro ($760-million) emergency aid plan to help Greece and other member countries, the first time humanitarian aid has been used within Europe.

Greece has been the main point of entry for the 1.13 million migrants who have arrived in the EU over the past 14 months.

The United Nations has warned of a looming humanitarian crisis on the Greek-Macedonian border, where aid agencies have reported a lack of food and tents and warned that the wintry weather is taking a toll on people's health.

Meanwhile in the northern French port of Calais, a group of Iranian migrants sewed their mouths shut in protest at the demolition of the so-called Jungle migrant camp, which is a magnet for people hoping to reach Britain.

The Calais situation topped the agenda at talks between French President Francois Hollande and British Prime Minister David Cameron in northern France on Thursday.

Hollande warned of "consequences" for the management of migrants with Britain if the country votes to leave the European Union.