Cyprus has been divided since a Turkish invasion in 1974 triggered by a brief Greek-inspired coup. UN-sponsored peace talks between Turkish Cypriots and Greek Cypriots have stumbled since they were relaunched in 2008 (see 'Background').
"It is an option to freeze ties with the EU presidency, with the Greek Cypriot side," Egemen Bağış told TGRT broadcaster.
"We don't have any relations with the Greek Cypriot side anyway, we don't recognise them, so we have no ties. I think that's what the foreign minister meant," he said in an interview.
Bagis appeared to be clarifying earlier comments by Turkey's Foreign Minister Ahmet Davutoğlu, who told a news conference: "If the Greek Cypriot side stalls negotiations and takes over the presidency of the European Union in July 2012, this means not only a deadlock on the island, but also a blockage, a freezing point in Turkey-European Union relations."
Bağış, Turkey's former EU negotiator who was appointed to the newly-created position of EU minister in Prime Minister Tayyip Erdoğan's government, said:
"But we will continue our relations with the [European] Commission, and if Greek Cypriot side tries to take advantage of the presidency and blocks new chapters, let it be."
Greek Cypriots represent the island internationally and in the European Union, while Turkey is the only country to recognise the Turkish Cypriot state.
Under the EU's Lisbon treaty, which established in Brussels a permanent head of the European Council - which groups national governments - and a new foreign and security policy chief, the rotating presidency has lost some importance but a determined country can still shape the agenda.
Of the 35 'chapters' - policy areas of EU law - Turkey has completed one, and 18 have been frozen because of opposition by EU member states including Cyprus and France.
EurActiv with Reuters