Greece said the two soldiers - a lieutenant and a sergeant - accidentally strayed into Turkey during a patrol of the Greek-Turkish border, due to bad weather.
The development is likely to aggravate the already strained relations between the neighboring countries.
The court chose to remand them in custody on Friday, on the grounds of attempted military espionage and entering a prohibited military zone, Turkish media said. A lawyer for the soldiers had requested their release earlier on Monday, according to CNN Turk.
Prior to Monday's court decision, Greece called on Turkey to comply with worldwide law.
The soldiers, detained near the Pazarkule district, said bad weather had led to their getting lost.
Greece said in January it would not extradite eight Turkish soldiers who fled there after a failed 2016 coup attempt against President Tayyip Erdogan.
A Turkish court on March 2 placed the two Greeksoldiers under arrest on espionage charges after they illegally crossed into Turkey, state media reported, in a move that risks a new flaring of tensions between Ankara and Athens.
"We are in consultation with Turkish authorities for a prompt resolution of the matter", Greek government spokesman Dimitris Tzanakopoulos told reporters.
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