The EU on Monday said it failed to reach any "concrete solutions or compromises" with Turkey in talks with President Recep Tayyip Erdogan seeking to fix their tattered relations.
And a row over Greece and Cyprus that erupted last week has added another point of contention just days before the talks.
"EU membership continues to be our strategic target", Erdogan said. The EU has already committed €3 billion to help Turkey manage the refugee influx and another €3 billion is on the way.
The meeting was hosted by Bulgarian Prime Minister Boiko Borissov, whose country now holds the rotating Presidency of the Council of the EU, and attended by Turkish President Recep Tayipp Erdoğan, Tusk, and European Commission President Jean-Claude Juncker.
Turkey said last week that the PKK is creating a base in Sinjar, and that Turkish forces would attack it if necessary.
But he added that "we will have a frank and open debate with President Erdogan".
The EU accounts for about half of Turkish exports.
On November 22, 2017, Presidents of Russia, Iran and Turkey, Vladimir Putin, Hassan Rouhani and Recep Tayyip Erdogan, had a meeting in Russia's Sochi to announce considerable progress in joint anti-terrorist campaign in Syria and the beginning of a new stage in the settlement of the crisis in this country.
Ankara and Brussels had in March 2016 agreed a controversial deal to stop the flow of migrants, in what was seen as a landmark in cooperation and which Turkey hoped would yield visa free travel to Europe.
Another EU meeting in Brussels a week prior had ended with EU leaders condemning Turkey for the arrest.
The PKK is listed as a terrorist organization by Turkey as well as the US and the EU.
Erdogan has alarmed the West with a massive purge of hundreds of thousands of civil servants and political opponents since a failed coup in July 2016, including the arrest of dozens of independent journalists on trumped-up charges. European Union leaders have made clear that any further accession discussions are on hold. "As you know, it was a long list including the rule of law and press freedom in Turkey, and Turkey's bilateral relations with member states, also the situation in Syria", he said.
"I hope that we have left a tough period in the relations between Turkey and Europe behind us", Erdogan said and voiced hope that "a first step was taken here toward restoring trust with Europe".
Ankara's long-stalled bid to join the European Union will also be discussed during the summit, but Western diplomats and analysts agree meaningful steps are unlikely.
"It would be a mistake for a Europe that claims to be a global power to keep Turkey outside of expansion policies", Erdogan said.