* EU leaders cite growing divide between Brussels and Ankara
* Turkey want stalled EU membership talks wrapped up soon (Updates with end of summit)
VARNA, Bulgaria, March 26 (Reuters) - European Union leaders said talks with Turkish President Tayyip Erdogan on Monday offered no answers to a long list of concerns including over Turkey's intervention in Syria and the jailing of journalists at home.
At a summit that host Bulgaria described as "charged with great tension", the bloc vowed to keep funds flowing for a refugee deal with Ankara, but disappointed Turkish demands for deeper trade ties or visa-free travel to Europe.
Despite criticism from European governments of what many view as Erdogan's growing authoritarianism, EU leaders left the door open to Turkey's stalled bid for membership to the bloc, but said only he could act to remove the obstacles to accession.
"I raised all our concerns, as you know it was a long list", European Council President Donald Tusk told reporters after the talks held in the Black Sea port city of Varna.
"If you are asking me if we achieved some solutions or compromises - my answer is: no," he added. "Our position is clear - only progress on these issues will allow us to improve EU-Turkey relations, including the accession process".
Erdogan, who has alarmed the West with a massive purge since a failed coup attempt in July 2016, remains an important ally in the U.S.-led NATO alliance, the fight against Islamic militants and as a destination for many Syrians fleeing war.
Turkey shares borders with Iraq and Syria as well as influence with Russia in the Black Sea region, but the EU is still its biggest foreign investor and trading partner.
EU leaders cited these geostrategic interest as common ground for greater cooperation with Turkey, despite differences.
"While our relationship is going through difficult times, in areas where we do cooperate, we cooperate well," Tusk told reporters.
Over a two-hour dinner of "Slav salad", turbot fished from the Black Sea and local wines, Erdogan said he pressed EU counterparts for progress in talks on letting Turks visit Europe without visas and a deeper customs union.
"We hope to have left the difficult times with the EU behind", Erdogan said. "Turkey and the EU are long-term strategic partners. It would be a serious mistake for the bloc to push Turkey out of its enlargement politics".
Only on Erdogan's plea for EU funds under a March 2016 deal to take in migrants fleeing the country's war did the bloc's leaders convey their full support.
However, on the issue of Turkey's membership negotiations, which began in 2005, then stalled for five years and have now effectively collapsed, they seemed to be talking past each other.
Brussels considers the EU membership bid a separate process focused on rule of law, press freedoms and economic reforms. EU officials say Turkey's post-coup crackdown on civil rights has taken it further from complying with EU membership.
Objections to Turkey's military sweep northwest into Syrias Afrin region and a standoff over Mediterranean gas with EU members Greece and Cyprus have added to grievances.
Erdogan has also made more foes in Europe in the past year over what some view as hostile rhetoric, including comparing the Dutch and German governments to Nazis, with some calling for an end to accession talks. ($1 = 0.8063 euro) (Additional reporting by Robin Emmott in Brussels and Tulay Karadeniz in Varna; writing by Alissa de Carbonnel and Robin Emmott; editing by John Stonestreet and G Crosse)