Speaking to the private television channel, Skai, the lawyer who represented the soldiers, said they denied involvement in the failed coup, but feared an unfair trial if they were to be extradited to Turkey, Efe news reported.
At least 265 persons died in clashes during the failed coup that started on Friday night. Of them, 161 were civilians and police officers, while 104 were alleged coup supporters.
The Turkish government has since launched a wave of mass arrests, nearly 3,000 alleged coup-plotters have been detained.
A few hours after the soldiers landed the Black Hawk helicopter at Alexandroupoli airport, in north-east Greece, Turkish Minister for Foreign Affairs Mevlut Cavusoglu called on Athens to immediately extradite the "traitors".
Greek Foreign Minister Nikos Kotozias said that it would be difficult for the soldiers to obtain asylum in Greece, considering that they have been accused of complicity in the attempted coup.
More than 1,000 people across Turkey were injured in the clashes.
Cities across Turkey held pro-democracy demonstrations on Saturday night.
Since the beginning of the failed coup, Erdogan has repeatedly asked the Turkish population to take to the streets in order to demonstrate against the coup and "defend democracy".
The head of the Turkish counter-terrorism police unit, Turgut Aslan remained in a critical condition in hospital on Sunday, after sustaining a gun shot to the head during the clashes.
The international community unanimously condemned the attempted coup and has called for stability.
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