"We are in communication with Turkish authorities to swiftly settle the issue", Tzanakopoulos said.
It is understood that previous incidents have normally been resolved on the spot, Reuters reported.
The two Greek soldiers who were detained after accidentally crossing the Turkish border in bad weather on Thursday will appear before a court on Monday on charges of illegally entering a prohibited military zone, but not for espionage, as initial media reports had suggested, Ekathimerini writes.
Athens said the two soldiers accidentally strayed into Turkey because of bad weather - heavy snow and fog had been reported in the area.
Turkish officials were not immediately available for comment, the agency reported.
"There was no fighting and [the soldiers] are now in Edirne", Greek military command spokesman Nikolaos Fanios told Agence France-Presse, adding that the pair are in good health.
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The troops were patrolling the area around the Evros river that separates the two countries, Fanios said.
"The Greek foreign minister is now arranging for their repatriation", he added.
Greece and Turkey are North Atlantic Treaty Organisation allies, but their bilateral relations are often strained over an array of territorial disputes.
Ankara's ties with the European Union are going through a particularly rough patch, following Turkish President Recep Tayyip Erdogan's threat to block gas drilling in the Mediterranean around Cyprus.
On 13 February, a Turkish vessel collided with a stationary Greek coastguard boat off of the contested Imia islets that both countries claim territorial rights to.
Meanwhile, Ankara has also been angered by a recent Greek court decision not to extradite eight Turkish nationals who fled the country following the 2016 failed coup attempt. The Turkish military, however, says it needs to do more investigating, which is code for whether the two might have been spying.