ATHENS (Reuters) - Greece on Sunday rejected any suggestion of a trade-off for the release of two Greek soldiers it says are being unjustifiably held by Turkey in a case that has deepened strains between the two NATO allies.

FILE PHOTO: Greek Prime Minister Alexis Tsipras attends a cabinet meeting at the parliament in Athens, Greece April 3, 2018. REUTERS/Costas Baltas/File Photo

The rhetoric between the two neighbors with deep-rooted historical disputes has sharpened, with two Greek soldiers detained by Turkey and eight Turkish soldiers seeking asylum in Greece the focal point of verbal jousting in recent months.

The Greek soldiers were arrested in March after crossing a borderline between the two countries and face charges of illegal entry in Turkey.

The eight Turkish commandos, who commandeered a helicopter to flee Turkey as a coup against President Tayyip Erdogan crumbled in July 2016, have sought asylum in Greece. Turkey says they were involved in the putsch and demands they be returned to face trial.

“Concerning references to an exchange ... between the matter of the Greek soldiers and other issues, we stress once more that it is unacceptable and is rejected,” a statement from the office of Greek Prime Minister Alexis Tsipras said.

“The position of Greece, and of the EU in its entirety, is clear and consistent: we seek the immediate release of the two Greek soldiers without conditions,” it added.

In an interview with private broadcaster NTV on Saturday, Erdogan appeared to float the possibility of handing over the two soldiers if Greece returned the eight Turkish commandos.

“If you want this to be discussed around (the) table, you will return the coup plotters,” Erdogan said, adding he had raised the issue during an EU summit in Bulgaria in March.

Greek courts have repeatedly rejected Turkish requests to extradite the group, most of whom remain under protective custody. Turkey says Greece is a haven for its enemies.

The two Greek soldiers, Erdogan said, had violated Turkish borders.

Turkey and Greece are at odds over issues ranging from airspace over the Aegean Sea, sovereignty over islets and the ethnically split island of Cyprus. They almost went to war over an uninhabited islet each claims as its own in 1996.

Controversy was recently rekindled when Greek youths hoisted a flag on another rocky outcrop..