Turkey says ready for talks with Greece without preconditions
But the olive branch came as the two uneasy NATO allies' navies conducted separate exercises close to each other just south of Crete in a mutual show of force.
"We are in favour of negotiations for fair sharing but nobody should lay down preconditions. This cannot happen with preconditions laid down by Greece," Turkish Foreign Minister Mevlut Cavusoglu said after talks with his German counterpart Heiko Maas in Ankara.
EU powerhouse Germany is spearheading efforts to avoid an outright military conflict that could imperil Europe's future access to newly-discovered energy reserves.
Maas shuttled between Athens and Ankara on Tuesday in a bid to get the sides to temper the rhetoric and re-enter direct talks.
After both visits were over, Maas conceded that the dispute had entered a "very critical" phase.
Nevertheless, "no one wants to solve this issue in a militaristic way," Maas said through a translator, "and there is a willingness on both sides for dialogue."
Cavusoglu praised the German mediation effort but said Ankara made a good faith gesture by announcing a pause to its exploration activity last month.
"I would like to advise Greece ... to abandon its spoilt (action)," Cavusoglu said.
On Sunday, Turkey announced a decision to extend its exploratory ship Oruc Reis's mission by an extra four days to Thursday, which prompted an immediate Greek response to carry out naval exercises nearby.