Migrants living in overcrowded camps on Greek islands are to be offered €2,000 to return voluntarily to their countries.
A financial aid deal agreed between the European Union and Greece on Thursday is intended to encourage some 5,000 migrants to leave Greece, which has borne the brunt of migrants seeking asylum in Europe.
"We have agreed on a temporary voluntary return programme for a period of one month", said Ylva Johansson, Commissioner for Home Affairs.
This programme will be accompanied "by an allowance of €2,000 which will help people to reintegrate in their country of origin", she added.
Only those who arrived before 1 January are eligible for the programme, which Johansson said was a means for "reducing the pressure of overcrowding" in the camps on the Greek islands.
Squalid conditions on Greek islands
More than 37,000 people are living in overcrowded camps on five Greek islands in the Aegean Sea, the main gateways for asylum seekers to Europe from the nearby Turkish coast.
Seven European Union member countries have already announced the possibility of housing at least 1,600 migrant children living in Greece, according to the commissioner.
"We are not very well prepared, we still lack a common policy on migration and asylum policy and I am working on this," said Ylva Johansson, stressing that she would announce her proposals in April.
These voluntary returns will be carried out with the assistance of the International Organisation for Migration (IOM) and the European border control agency, Frontex.
The programme does not apply to asylum seekers who recently arrived in Greece after Turkey announced on 28 February that it would allow migrants to leave for Europe.
Since that announcement, thousands of people flocked to the Greek-Turkish border, resulting in violent incidents involving Turkish and Greek police forces.
In order to deter further migration, Greece had adopted a series of controversial measures in the wake of the incident, including the suspension of the asylum procedure and compulsory return of migrants.