Greek minister of immigration policy Loannis Mouzalas declared the country's intention to speed up the procedure to send back migrants to Turkey in the coming weeks, if they did not qualify for asylum.
Amid criticism, Mouzalas complained about what she believes to be an inefficient slowness of the expulsion process.
Turkey recently signed a deal with the European Union (EU) which aims at closing off the main route used by about a million refugees and migrants last year.
Ankara has agreed to take back all the migrants currently living in Greece and not entitled to asylum. In return, the EU will provide funds worth $3.7 billion and will open negotiations for Turkey's admission in the union.
Medical aid charity Medecins Sans Frontieres said on Friday it will reject all funding from the European Union and its member states. An action carried on in protest against the EU-Turkey deal that the organisation considers responsible for "jeopardising the very concept of the refugee."
She said Greece has deported 468 people back to Turkey none of whom had requested asylum. Just two Syrian refugees have been ordered back and they are appealing in court against the decision.
"It would constitute failure if within the next month-and-a-half those who are obliged to leave the islands didn't do so," Mouzalas told Greek TV.
The minister attitude reflects a change of approach in Greek policies towards immigration. Greece was until now one of the most accessible countries in Europe for migrants.
Greek parliament recently voted to replace two civil society members of an asylum appeal board with judges.
As many as 100,000 immigrants are believed to have reached Greek shores in the past two years. The Mediterranean country is caught in a consistent economic crisis and sustaining the cost of the mass migration against Syrian Civil War has become more and more difficult.
About 8,400 migrants are currently living in the country's islands and half of them have expressed interest in applying for asylum, overwhelming the system.
The situation in Greek camps is tense. Earlier this month, migrants set tents on fire, lamenting to have been stranded there since March, brawled with each other.