But leaders acknowledge there is no silver bullet and face many obstacles over the next two days, from howls of outrage that they plan mass expulsions of vulnerable people to a country with a patchy and worsening human rights record, to a lingering feud between Ankara and small but vocal EU member Cyprus.
"Work is progressing but there is still a lot to do," European Council President Donald Tusk wrote to leaders inviting them to the summit he will chair. After discussing the economy, the 28 EU national leaders will discuss the migration issue over dinner, starting around 8 p.m. (1900 GMT).
A breakfast is set for Friday with Turkish Prime Minister Ahmet Davutoglu, where Tusk hopes to finalize a deal which the Turkish premier first sprang on the EU, with backing from German Chancellor Angela Merkel, at a special summit 10 days ago.
Under the deal, which was set out in fuller fashion by Tusk in a draft for EU leaders on Wednesday, Turkey will, in addition to a previous agreement to try and prevent the smuggling of migrants via rafts, take back all those, including Syrian refugees, who do make it to Greek islands off Turkey`s coast.
The draft, which was seen by Reuters, says the plan is "to break the business model of the smugglers and to offer migrants an alternative to putting their lives at risk". It stresses the plan is "a temporary and extraordinary measure which is necessary to end the human suffering and restore public order".
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