The two NATO countries have long-standing sea and air boundary disputes.
Greece and Turkey have accused each other's military of repeatedly violating their country's airspaces.
Turkey claimed on Thursday that fellow NATO member Greece had entered Turkish airspace "thirty times in three days".
The accusations came just one day after Greek Prime Minister Kyriakos Mitsotakis had made a similar claim against Ankara.
Mitsotakis had stated that Turkey's military had been conducting unauthorised flights over several large Greek islands
Turkey's foreign ministry rejected the allegations and has insisted that Greece’s air force had carried out “provocative flights” near Turkey’s coastal towns of Didim, Datca and Dalaman.
The two countries have long-standing sea and air boundary disputes amid moves to explore potential undersea natural gas reserves.
The disagreement has resulted in near-daily air force patrols and interception missions, mostly in the disputed airspace around Greek islands that are near Turkey’s coastline.
Mitsotakis said on Thursday that he had contacted NATO Secretary-General Jens Stoltenberg to report the alleged airspace violations by Turkey.
“I made it clear... that this type of behaviour by a NATO ally in the southeast flank of the alliance is simply unacceptable,” Mitsotakis said.
"It undermines European security as well as the unity of purpose of NATO," he added.
Turkey's ambassador to Athens was also summoned by the Greek foreign ministry on Wednesday to receive a formal complaint.
Turkey’s Foreign Ministry called on Greece to “stop provocative actions and rhetoric” and to support recently-resumed talks that aim to build confidence between the two countries.
“While Greece is the party which started and escalated the tension — accusing our country of unfounded allegations is incompatible with the recent positive agenda and good neighborly relations between the two countries,” the Turkish ministry said in a statement.
“There is no change in Turkey’s attitude toward resolving all Aegean disputes, including the width of the airspace, within the framework of a sincere dialogue, in accordance with international law."
Greek Prime Minister Kyriakos Mitsotakis met in Istanbul with Turkish President Recep Tayyip Erdogan last month after Russia’s invasion of Ukraine became an urgent topic among NATO allies.