Turkey and the European Union must still resolve a "catalogue of issues" on a planned migration deal, EU President Donald Tusk said Tuesday, after shuttling between Nicosia and Ankara in an effort to overcome objections.

The deal is at the heart of the EU's response to a migration crisis that saw more than 1 million migrants and asylum seekers reach its shores last year, stretching resources thin and creating tensions. More than 152,000 other migrants have arrived this year so far.

The agreement with Turkey, which was first outlined at a summit last week, would offer progress on the country's long-running bid for EU membership and concessions on visa-free travel to Europe, in exchange for help from Ankara in stemming migrant flows over the Aegean Sea.

Brussels and Ankara had hoped to finalize the deal by Friday, when Turkish Prime Minister Ahmet Davutoglu is to meet EU leaders for a second round of talks in two weeks. But the plan has run into legal hurdles and objections out of several EU capitals.

"It is clear that there is still hard work to be done" to make the proposal legally sound, practically implementable and acceptable to all 28 member states and to Turkey, Tusk said in Ankara following talks with Davutoglu.

"This is not an easy task, and we have to get it right," Tusk added.

Earlier Tuesday, Cyprus threatened to veto part of the deal, arguing that Ankara had failed to fulfill past obligations related to its bid for EU membership.

Cypriot President Nicos Anastasiades complained specifically about Turkey referring to Cyprus as a "defunct" state and refusing to recognize it as a country.

The island nation has been split since 1974 between a Greek south and a Turkish north. Eight negotiating chapters under Turkey's EU accession bid have been blocked for years as part of an attempt to pressure Ankara into finding a solution for Cyprus.

"The Republic of Cyprus does not intend to consent to the opening of any chapters if Turkey does not fulfill its obligations as described in the negotiating framework and the Ankara protocol," Anastasiades said in Nicosia after talks with Tusk.

Anastasiades did not specify which obligations he was referring to. The EU-Turkey negotiating framework for instance calls for "progress in the normalization of bilateral relations between Turkey and all EU member states, including the Republic of Cyprus."

The island's Greek and Turkish communities re-engaged in peace talks last year. Anastasiades warned against creating any "confrontation" with Ankara just as those negotiations have gained traction.

The migration plan has also been slammed by rights advocates because of a provision that foresees the EU sending migrants from Greece back to Turkey, including Syrian refugees.

The return of migrants to Turkey would be a "temporary" measure, required to "end the human suffering and restore public order," according to revisions that Tusk is expected to propose to member states on Wednesday, seen by dpa.

According to the document, all migrants will be able to apply for asylum in Greece - as demanded by rights advocates - with unsuccessful claimants to be returned to Turkey.

Once the flow of migrants from Turkey to the EU has ended, the bloc would begin to directly take in Syrian refugees from the country, under the proposed revision.

Ahead of his trip to Ankara, Tusk expressed hope that the new migration deal can still be finalized at this week's summit, which begins Thursday.

"Hope never dies in Europe. We are now in talks and hope that we will come to a good solution," German State Minister Michael Roth said at preparatory talks in Brussels.

He added that he saw "no legal problems" with the deal.

But Spain has called the agreement "unacceptable," warning that it could violate international and European law. Trade unions and social organizations announced plans to hold protests against the deal on Wednesday across Spain.

Meanwhile, French Prime Minister Manuel Valls told parliament that cooperation with Turkey was "indispensable." But he added that "there cannot be the slightest blackmail ... the cooperation must respect European and international law."

Austrian Interior Minister Johanna Mikl-Leitner also voiced concerns over the proposed agreement, including the risk that the concessions on visa-free travel could lead to higher numbers of Turks seeking refugee protection in Europe.

In a letter to EU Migration Commissioner Dimitris Avramopulos - a copy of which was obtained by dpa - she also warned that countries like Morocco and Libya might demand a similar deal.

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