Greek judges have ruled that a Syrian asylum seeker should not be sent back to Turkey because it is not safe.
Amnesty International campaigners say the decision throws the EU-Turkey migrant deal into doubt.
They say migrants in Turkey do not have basic human rights and many are at risk of being taken to Syria.
A source at the Greek migration ministry said the judges were only deciding whether the individual's case could be heard in Greece or not.
On the same day the judges' ruling emerged, Greek and EU authorities sent back 51 migrants to Turkey on boats from the islands of Lesbos and Kos.
Under a deal struck between Turkey and the EU, migrants arriving in Greece are sent back to Turkey if they do not apply for asylum or if their claim is rejected.
The deal came into force in March, and more than 400 people have been sent back.
Now a Greek committee of judges has decided against sending a Syrian asylum seeker back to Turkey.
'The right approach'
Amnesty spokesman Giorgos Kosmopoulos told the BBC that Turkey was not currently protecting migrants and refugees to the standards of the Refugee Convention. "Until it becomes a safe country nobody should be returned there," he said.
Migrants in Turkey could not expect access to the rights to work, medical care or family life and there had been "widespread returns of Syrians back to Syria from Turkey", he added.
"The whole (EU) deal should stop and refugees should be settled in other European countries safely and with dignity," Mr Kosmopoulos said.
A civil war has been raging in Syria for more than five years.
The Syrian seeking asylum in Greece had initially been turned down by a Greek court and told he would be sent back to Turkey. However, he appealed against the decision to a panel of judges on the island of Chios who ruled in his favour.
The migration ministry official said that judicial committees at detention centres on the islands did not decide whether migrants were given asylum or not, but only whether Greece should examine their claims.
Key points from the agreement
- Returns: All "irregular migrants" crossing from Turkey into Greece from 20 March are sent back, and each arrival is individually assessed by the Greek authorities.
- One-for-one: For each Syrian returned to Turkey, a Syrian migrant is resettled in the EU. Priority is given to those who have not tried to illegally enter the EU and the number is capped at 72,000.
- Visa restrictions: Turkish nationals should have access to the Schengen passport-free zone by June. This will not apply to non-Schengen countries like Britain.
- Financial aid: The EU is to speed up the allocation of €3bn ($3.3 bn; £2.3 bn) in aid to Turkey to help migrants.
- Turkey EU membership: Both sides agreed to "re-energise" Turkey's bid to join the European bloc, with talks due by July.
A note on terminology: The BBC uses the term migrant to refer to all people on the move who have yet to complete the legal process of claiming asylum. This group includes people fleeing war-torn countries such as Syria, who are likely to be granted refugee status, as well as people who are seeking jobs and better lives, who governments are likely to rule are economic migrants.