A week after European and Turkish leaders reached an ambitious, if legally dubious, plan to address the refugee crisis by sending people back across the sea, obstacles to the deal were piling up on Wednesday, the eve of a summit that’s intended to finalize the pact.

The tentative agreement hammered out last week effectively shifts responsibility for the unparalleled flow of migrants into Europe back onto Turkey, the country through which most new arrivals travel on their way out of war zones in the Middle East and Asia.

In exchange for Turkey accepting returnees, Europe has promised billions of dollars in support — plus visa-free travel in Europe for Turkish citizens and revived negotiations to allow Turkey into the 28-member European Union. When the deal was struck, E.U. leaders described it as a potential game-changer after a year in which more than 1 million asylum-seekers landed on European shores.

But in the days since, doubts have been rising over whether either side can keep its end of the bargain.

The roadblocks range from withering assessments by human rights groups to the thorny implications of the pact for decades-old territorial disputes.

European Council President Donald Tusk, left, talks with Cyprus President Nicos Anastasiades at the Presidential Palace before their meeting in the ethnically divided island's capital Nicosia on Tuesday. (Petros Karadjias/AP)

The most acute threat that the deal could unravel altogether appeared on Wednesday to be coming from the island nation of Cyprus, one of the smallest E.U. members but one for which a warming of relations with Turkey is especially sensitive.

Cyprus has said it will block any attempt to advance Turkey’s E.U. membership until Turkey recognizes Cyprus as a state, something Ankara has steadfastly refused to do. The island has been divided since 1974 between a Greek Cypriot south and a militarized Turkish-controlled north.

Cyprus’s president, Nicos Anastasiades, was expected in Brussels Wednesday night for final talks before the continent’s other leaders arrive on Thursday. But as of Tuesday, he was showing little willingness to bend, making clear to reporters that he resented E.U. attempts to force him to back down on his veto threat.

The pressure, he said after a Tuesday meeting with European Council President Donald Tusk in the Cypriot capital of Nicosia, was “unwarranted, counterproductive and not to mention unacceptable.”

Even if Cyprus doesn’t ultimately scuttle the deal, myriad doubts remain, reflecting just how delicate the negotiations will be during the two-day summit that kicks off on Thursday.

A proposal to liberalize E.U. visa rules for Turkey’s 75 million citizens is especially problematic and could be blocked by a number of countries. The French government, for instance, is believed to be wary given the potential that the far-right National Front could exploit the issue as a security threat in the run-up to presidential elections next year. British campaigners for the country to exit the E.U. in a June referendum, meanwhile, have already begun highlighting a potential flood of Turkish travelers as one more reason why the U.K. should get out.

The visa change would also have to earn support from the European Parliament.

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The Turkish government is “therefore right to be doubtful as to whether the E.U. — despite the intentions and declarations of its leaders — can and actually will deliver visa-free travel,” wrote Mujtaba Rahman, Europe analyst with the Eurasia Group, in a recent research note.

The deal between Turkey and the E.U., Rahman concluded, “won’t last.”

The E.U.’s heavy reliance on Turkey as a solution to its refugee woes reflects the level of desperation felt in European capitals as repeated attempts to come to grips with the crisis have fallen flat.

The E.U. and Turkey first struck a deal in the fall under which Europe would pay about $3 billion in exchange for stepped-up Turkish efforts to halt the smuggling of migrants between Turkish and Greek shores.

But so far, there’s little evidence the plan is working: The number of people arriving by boat on the Greek islands this year has been 20 times higher than it was during the same period in 2015.

The preliminary deal reached last week adds an additional edge of deterrence, with Turkey agreeing to accept the return of all “irregular migrants” arriving in Greece. Europe has said it will resettle one Syrian refugee from Turkish camps for every Syrian who’s returned to Turkey.

European and Turkish leaders say the plan is meant to discourage people from making dangerous voyages that have claimed the lives of more than 400 migrants this year. But human rights groups have slammed the agreement, saying it would deny people the protections and asylum rights established under international and E.U. law.

In a letter to European leaders this week, Human Rights Watch Executive Director Kenneth Roth cited the “contradiction at the heart of this plan” between a fast-tracked, blanket return policy and the need to give each asylum-seeker individual consideration.

Even before the plan is finalized, European nations all along the migrant route reacted to its announcement last week by closing their borders — effectively trapping tens of thousands of people in Greece. They remained stuck there Wednesday, with little prospect of making it deeper into Europe.

But speaking from St. Peter’s Square on Wednesday, Pope Francis urged continental leaders to reconsider.

“How is it possible that so much suffering can befall innocent men, women and children?” he asked. “They are there at the border because so many doors and so many hearts are closed.”