Greek Prime Minister Kyriakos Mitsotakis said on Sunday that the reported departure of a Turkish gas exploration ship from the disputed eastern Mediterranean was "a positive step" after weeks of tensions with Ankara.
Escorted by Turkish warships, the Oruc Reis was deployed on August 10 to a region believed to be rich in natural gas and contested by both countries.
An outraged Athens deployed its own navy in response, staging exercises with allies.
Pro-government Turkish newspaper Yeni Safak reported that the vessel's mission had not been extended after ending Saturday.
Ship-tracking websites marinetraffic.com and vesselfinder.com both showed the vessel off the coast of Turkey near the port of Antalya on Sunday.
"This is a positive first step ... I hope there will be more of them," Mr Mitsotakis told reporters at a press conference in the Greek city Thessaloniki.
Yeni Safak reported that the withdrawal of Oruc Reis was "a step to give diplomacy a chance".
Athens "is always ready to begin exploratory contacts with Turkey," Mr Mitsotakis said Sunday.
The face-off across the Aegean Sea over maritime territory has pitched relations between fellow NATO members Greece and Turkey into a new crisis.
Already rumbling for several years, the latest escalation in the dispute drew several fellow EU countries to stand behind Greece.
France in particular sent naval forces to join Greece's military manoeuvres.
On Thursday, seven leaders of Mediterranean EU countries threatened Turkey with sanctions by the bloc if it did not end its "confrontational actions".