The dialog was held following a five-year hiatus on Monday, after Turkish Foreign Minister Mevlut Cavusoglu invited Greece to resume direct talks in his meeting with top EU officials in the Belgian capital Brussels last week.
Greek Prime Minister Kyriakos Mitsotakis said his country would join the talks with "optimism and hope" -- a comment echoed by Cavusoglu.
European Council President Charles Michel has welcomed the development, saying the bloc is "looking forward to progress resumption of exploratory talks between Turkey and Greece as well as the Cyprus settlement process”.
The meeting is not expected to make major headway since the two NATO countries have clashed over their agenda last week.
Greece wants to limit the discussions to continental shelf borders and the size of exclusive economic zones. But Ankara, which accuses Athens of illegally stationing troops on some of its islands, wants to discuss aerial zones.
"It's not right to choose one (subject) and say, 'we're holding exploratory talks on this'," Cavusoglu said.
Michael Tanchum of the University of Navarra and the Austrian Institute for European and Security Policy (AIES) said the process could be helped along if it involved a third party such as the United States or Germany.
"The likely outcome of such adjudication would invalidate the use of some small Greek islands near Turkey's mainland... while upholding the use of larger islands and more distant islands," Tanchum said.