The pair were arrested on Friday for entering a prohibited military zone in the northern province of Edirne.

Turkish media initially reported that the two men were arrested for "attempted military espionage", but Greek authorities denied it.

The soldiers told prosecutors last week that they had erroneously entered through a border crossing after "following footprints in the snow in an attempt to stop migrant smuggling", local media said.

Turkish Deputy Prime Minister Bekir Bozdag said on Monday that prosecutors wanted the two soldiers detained for attempted military espionage and entering a forbidden military zone, but the judge ordered their arrest only on the second charge.

The Greek army said the lieutenant and sergeant lost their way in poor weather while patrolling around the Evros river that divides the two nations.

Greek Foreign Minister Nikos Kotzias, speaking before the court's decision, urged its NATO ally Turkey "to apply the provisions of international law and not turn a routine procedure into a major legal and political problem".

Relations between Ankara and Athens are tense over a number of issues including the Greek failure to extradite eight Turkish troops who escaped Turkey by helicopter on the night of the July 2016 attempted overthrow of President Recep Tayyip Erdogan.

But Bozdag told reporters in Ankara "there was no question of an exchange" for the Turkish military personnel, echoing comments made at the weekend by Athens.

"We are not at war with Turkey to conduct an exchange of prisoners," junior foreign minister Yiorgos Katrougalos said Saturday.

Turkish and Greek vessels have also in the last weeks twice collided off Aegean islets that have been a historic flashpoint in a long-running demarcation dispute.

Tensions are also high over Cyprus as Turkey promises to prevent attempts by the internationally recognised Greek Cypriot government to exploit oil reserves off the Mediterranean island.

The northern part of the island is still occupied by Turkish troops following the 1974 invasion in response to an Athens-inspired coup aimed at uniting it with Greece.