European Union leaders demanded that Turkey show them some respect on Thursday and warned its encroachment into Greek waters is "completely unacceptable".
The 27 national leaders met by videolink to discuss the coronavirus pandemic, but European Council chief Charles Michel said they also discussed the stand-off in the Mediterranean.
Turkey has deployed a research ship to search for gas in waters claimed by Greece, setting off a fierce war of words with European leaders and talk of sanctions.
NATO has set up a hotline to help the Greek and Turkish militaries avoid accidental clashes, and Germany has been leading a diplomatic outreach.
But Greece and Cyprus, with strong backing from France, have been calling for tougher action. The EU leaders are due to return to the issue at their next summit.
"We expressed our determination to be respected and we agreed to work on two tracks, a positive track and a less positive one," Michel said.
"We offered a clear way to work towards a positive agenda with Turkey. So far Turkey has not chosen this path," he said.
"We condemn the recent unilateral action in the eastern Mediterranean, provocations and rhetoric which are completely unacceptable," he warned.
"We will have the occasion to revert to this topic in December," he said, referring to the next scheduled EU summit, at which the 27 could decide on action.