German Chancellor Angela Merkel has urged Turkey to lift its boycott of Cyprus, during a visit to Ankara.
Mrs Merkel has expressed doubts over Turkey joining the EU
She said it was a "necessary condition" for progress in talks on Turkey's accession to the European Union.
However, Turkey's prime minister said there was no chance of that happening until the EU eased its own embargo on Turkish-occupied northern Cyprus.
Turkey does not recognise the government of Cyprus, which became an EU member in 2004.
But the EU wants Turkey to fulfil the terms of a customs union agreed between the two, and open up its airports and ports to Cypriot planes and ships.
Germany takes over the European Union's presidency in January.
Mrs Merkel has in the past said that normalising ties with the government in Cyprus is central to Turkey's relationship with the EU.
"It is a problem we must address... It is a necessary condition for progress with the EU negotiations," she said.
But Turkish Prime Minister Recep Tayyip Erdogan said: "We will never look positively at opening our ports and airports unless the isolation of the Turkish Cypriots is lifted."
Cyprus has been split since 1974, when Turkish troops invaded the north of the island after a Greek-inspired coup.
Mrs Merkel has said in the past she favours a "privileged partnership" rather than full EU membership for Turkey.
Mrs Merkel paid her respects to Ataturk
The EU has said Turkey must make widespread reforms to bring it into line with European conventions before it can join the EU.
Opinion across the EU is split over Turkey, with some supporting its membership but others strongly opposed.
The European Commission will issue a progress report on its membership talks next month.
Warning to sceptics
Commission president Jose Manuel Barroso warned EU countries on Thursday that suddenly blocking Turkey's entry would leave the bloc open to charges of "arrogance or even Islamophobia".
"If you ask me: can Turkey become a member of the EU today, the answer is no. But in 15, 20 or 25 years, who can say what the situation will be in Turkey and in Europe?" he added.
Earlier in the week EU enlargement commissioner Olli Rehn said advocating a "privileged partnership" rather than full membership weakened the EU's credibility.
Mrs Merkel met Mr Erdogan shortly after her arrival and paid her respects at the mausoleum of Mustafa Kemal Ataturk, modern Turkey's founder.
She is to stay in Turkey for two days, during which she is also due to meet Jewish, Muslim and Christian leaders.