Athens must make "significant" progress before asylum seekers who passed through Greece to other EU member states can be returned there, the bloc's executive said Wednesday.
Under the European Union's Dublin rules, asylum seekers must file their request in the first EU member state they reach, but two European courts have ruled that people should not be returned to Greece because of poor asylum conditions there.
Restoring the EU's asylum system has been seen as a key priority to tackle an influx of migrants and asylum seekers after more than 1 million people reached the continent last year. Greece was one of the main entry points, as its islands are reachable by boat from Turkey.
In February, the European Commission recommended several steps that Athens must take to improve its reception conditions for migrants and asylum seekers and to strengthen its borders. The EU has since struck a deal with Turkey, reducing new arrivals to a trickle.
"While the challenges and pressure of the migration crisis have continued in recent months, Greece has achieved undeniable progress in improving its asylum system and providing better conditions," EU Migration Commissioner Dimitris Avramopoulos said in a statement.
But the commission laid out several concrete steps that Greece must take, including the creation of more open reception facilities, improving access to asylum procedures, providing free legal aid and supporting the most vulnerable, including unaccompanied children.
Greek media reported earlier Wednesday that the country had granted asylum to 800 refugees on the island of Lesbos despite the migration deal struck between Turkey and the EU.
Under the agreement, migrants who arrived on the Greek islands after March 20 can have their asylum applications turned down and be returned to Turkey on the basis that it has been deemed a safe country and that they should apply for asylum there.
But many asylum courts in Greece do not consider Turkey a safe third country to which asylum seekers can be returned, according to the Greek daily Kathimerini.
Before the EU-Turkey deal, virtually no migrants passing through Greece sought shelter there, as many aimed to reach wealthier European countries such as Germany and Sweden.