Migrants protest at the barricaded border between Greece and Macedonia, which has allowed only a trickle of people to cross. (Vadim Ghirda/AP)

A senior European Union official carried a stark warning Thursday to the front lines of the migrant crisis, telling those seeking to flee poverty and unrest that Europe is no longer the answer, even as about 1 million migrants have now poured into Europe in the past year.

“Do not come to Europe,” said Donald Tusk, president of the European Council, after meeting with the Greek prime minister in Athens. “Do not believe the smugglers. Do not risk your lives and your money. It is all for nothing.”

Tusk’s comments came as a top U.N. official also warned Thursday that as many as 70,000 people could be “trapped” in Greece in the coming weeks because Macedonia and other European countries are shutting their borders, transforming Greece into a holding pen for migrants desperate to leave.

Tusk also said it was up to Turkey, not its European neighbors, to decide how to manage a reduction in refugee numbers — a stance that Turkish Prime Minister Ahmet Davutoglu quickly rebuffed. Turkey is under pressure to reduce the numbers of migrants crossing into Greece as a March 7 summit meeting between Turkey and the European Union approaches to discuss the issue.

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In the past week, unrest has broken out among the more than 30,000 refugees and migrants that Greek officials say are stranded at Greece’s blocked Macedonian border.

There was also violence at a makeshift camp being dismantled in northern France. And on Thursday, British Prime Minister David Cameron and French President François Hollande held talks in Amiens seeking to contain the migrant crisis in northern France, where thousands of refugees are camped in squalid conditions just over two hours from London and Paris.

The talks in Amiens came days after French authorities began demolishing sections of the infamous “Jungle” encampment in Calais, home to an estimated 4,000 migrants from North Africa and the Middle East, most of whom are seeking to reach Britain.

Turkish officials have long insisted that the West and others must share the financial and ­humanitarian burdens. And in November, Turkey signed a deal with the E.U. to stem the flow of migrants to Europe. In return, the E.U. agreed to provide 3 billion euros ($3.26 billion) to help the country deal with the migrant crisis and to accelerate talks about Turkish membership in the union.

On Wednesday, the E.U. announced plans for an emergency 700 million euros ($763 million) in humanitarian aid, but leaders across the continent are still struggling to manage the largest immigration crisis on European soil since World War II.

The meeting between Hollande and Cameron took on added dimensions after France’s economy minister was quoted as saying that border controls could be lifted if Britain leaves the E.U., opening up a potential path for migrants seeking to cross the English Channel.

With thousands of migrants stuck at the Greek-Macedonia border and 2,000 arriving daily, authorities warn that the stranded migrants could surge to 70,000 in a matter of days. (The Washington Post)

In a news conference Thursday, Hollande took several minutes to arrive at the subject of Calais. Despite the tear gas French police have used against migrants this week — and beatings that have been recorded on social media — it is imperative, he said, that the migrants who remain “be welcomed with dignity.”

Paris has requested more ­financial aid from London in managing the crisis. In advance of the summit, Harlem Désir, France’s secretary of state for European affairs, announced Thursday on RFI radio that the figure will include an additional 20 million euros ($21.8 million) — on top of the current 60 million euros ($65.4 million).

The extra funds, Désir said, will help with “securing the access area to the [English Channel] tunnel and Calais port area” as well as “the fight against smuggling networks.” Cameron said Thursday that the precise figure will be 17 million pounds ($24 million).

Echoing a rising sentiment across Europe, Cameron described the money as an expression of his government’s confidence in French border controls near the camps. “People should know that if they come to Calais, that is not a waiting room for getting into the United Kingdom,” he said. “We have strong borders, and it’s very important people understand that.

“They should be seeking asylum in France, and if they’re not asylum seekers, they should be returning to the countries from which they came,” he added.

Despite the immediate focus on the Calais camp crisis, the summit in Amiens was also an attempt by both leaders to illustrate the imperative of Britain remaining in the E.U. Britain is scheduled to hold a referendum in June on whether to leave the 28-nation bloc.

Before Thursday’s talks began, Emmanuel Macron, the French economy minister, told the Financial Times that if Britain votes to leave, the French could end a deal that allows border controls to be carried out in France.

“The day this relationship unravels, migrants will no longer be in Calais,” Macron said. Campaigners for a British exit from the E.U., dubbed “Brexit,” dismissed the warnings as “propaganda.”

Bernard Jenkin, a Conservative lawmaker who is campaigning for Brexit, told BBC Radio 4’s “Today” program: “What we are having now is propaganda being produced by other European governments at the request of the prime minister to try to scare people.”

But Macron’s comments suggest that Cameron’s warnings were not entirely political. Brexit would not automatically lead to a change in the border agreement between the two countries. Last year, for instance, Bernard Cazeneuve, France’s interior minister, said that tearing up the current agreement with Britain would be “a foolhardy path, and one the government will not pursue.”

Hollande urged the people of Britain not to leave. “I don’t want to scare you,” he said, “but there will be consequences if the U.K. decides to leave the E.U.”

Adam reported from London. Brian Murphy in Washington contributed to this report.

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Today's coverage from Post correspondents around the world