The troops were released on Monday after an order extending their custody expired. A decision on their asylum applications is still pending.
“We have a bilateral re-admission agreement, we have suspended that re-admission agreement,” Foreign Minister Mevlut Cavusoglu was quoted as saying by state-run Anadolu news agency on Thursday.
He said a separate migrant deal between the European Union and Turkey would continue.
Under the bilateral deal signed in 2001, 1,209 foreign nationals have been deported to Turkey from Greece in the last two years.
Cavusoglu said he believed the Greek government wanted to resolve the issue with the Turkish soldiers, but Greek judges were under pressure from the West.
Turkey has repeatedly called for the extradition of the suspected coup-plotters. Greek courts have rejected the requests and the soldiers have denied any wrongdoing, adding they fear for their lives.
The soldiers arrived to Greece on board a stolen military helicopter hours after the failed coup that killed hundreds and wounded thousands.
Turkish soldiers and tanks took to the streets in July 2016 as explosions rang out in Ankara and Istanbul. Turkish fighter jets dropped bombs on their own parliament.
After the putsch was quickly put down, a state of emergency was imposed under which more than 150,000 people were taken into custody with 110,000 civil servants dismissed, according to recent European Commission report.
Turkey’s Western allies have repeatedly condemned the Turkish government’s detentions and purges, and rights groups accuse Ankara of using the coup d’etat as a pretext to silence opposition in the country.
The government says the purges and detentions are in line with the rule of law.