Hahn and EU diplomatic chief Federica Mogherini meet Turkish Foreign Minister Mevlut Cavusoglu and Turkish EU Affairs Minister Omer Celik.
On the eve of talks in Brussels with senior Turkish officials, EU Enlargement Commissioner Johannes Hahn warned the country that is a candidate to join the bloc is "slipping away from European values."
"I am always concerned if there is an increase of tension between one of our member states or some member states with neighbouring countries. I think Turkey should understand the reasons for that and address it," Hahn told reporters.
"We are in the middle of the tourism season; this is certainly not conducive to invite people to come and go there," he said.
"The same applies for investment in the country, if the situation seems to be still very shaky, very unclear, very fragile."
Hahn and EU diplomatic chief Federica Mogherini meet Turkish Foreign Minister Mevlut Cavusoglu and Turkish EU Affairs Minister Omer Celik on Tuesday amid increasingly sharp exchanges over Ankara's rights record and a crackdown after last year's failed coup.
Relations between Germany and Turkey in particular are at rock bottom, with the two NATO partners at odds over the arrest of several German nationals as part of the crackdown, and over access of German officials to a NATO base.
Turkey and the EU began formal membership talks in 2005 after years of foot-dragging by EU member states wary of admitting such a large Muslim country.
Progress remained slow and the negotiations came to a virtual halt last year as President Recep Tayyip Erdogan rounded up opponents in a massive crackdown following a failed coup.
Some EU member states, led by Austria, want the talks to be suspended outright, and there have been similar calls in Germany as the crisis with Turkey deepens.
Asked about the possible suspension of funding for candidate member countries, Hahn said that while he had a certain amount of "discretion" on the matter, the money could not be halted as long as the accession negotiations remained open.
"As long as this decision (to halt accession) has not been taken, these payments must continue," he said.
Separately, NATO said it was trying to resolve a dispute over access to the Konya airfield in central Turkey where Berlin has military personnel stationed.
"In an effort to find a solution, the Secretary General (Jens Stoltenberg) has now offered to arrange a visit for (German) parliamentarians to Konya airfield within a NATO framework," Cazalet said.
"Konya airfield is vital for NATO operations in support of Turkey and the Counter-ISIS (Islamic State) coalition. We hope that we can find a mutually acceptable solution as soon as possible."