Turkey must understand its behaviour is 'widening its separation' with the EU, the bloc's Foreign Policy Chief Josep Borrell said on Thursday.
He referred to recent statements by the Turkish President, who called for a 'two-state' solution in Cyprus earlier this week.
Borrell added that to get relations back on track would 'require a fundamental change in attitude' from Ankara.
"Time is running and we are approaching a watershed moment in our relationship with Turkey," said Borrell.
Turkey is officially a candidate for EU membership. However, it remains at odds with the bloc over migration, Cyprus and drilling in the Eastern Mediterranean.
The EU has threatened to impose sanctions on Ankara over its gas exploration at a meeting of EU leaders next month.