Officials say improved services mean it is appropriate to return individuals to Greece, under EU rules that state asylum seekers need to lodge their asylum application in the first country they arrive in.
The requirement had been suspended as Greece struggled to deal with large numbers of asylum seekers, many fleeing conflict in Syria.
But overcrowded and harsh conditions remain a problem, and humanitarian organisations have expressed doubts about whether Greek authorities are able to adequately support refugees.
On Tuesday Berlin said it had asked Athens to take back 392 individuals, while other countries including the UK, France, the Netherlands and Norway have said they will seek to transfer smaller numbers.
Boris Cheshirekov, a spokesperson for the UNHCR Greece, told Sky News that transfers would resume on a case-by-case basis, and that vulnerable groups such as disabled people and children would not be returned.
“The capacity of the Greek state has increased dramatically in the last year,” he said, explaining that transfers will depend on an “assurance” by the Greek government.
Authorities in Greece and other EU countries stress that only small numbers of people are likely to be sent back.
Last month fears of overcrowding and neglect in Greece were highlighted by a riot at a camp in Lesbos, while many aid organisations have said that refugees struggle to access healthcare, work and shelter.
George Kanaris, a welfare services coordinator at the Athens Solidarity Centre, told Sky News the situation in Greece was “not ideal” and expressed “strong doubts” that it was improving.
“It is not by chance they choose to leave the country”, he said, explaining that tough conditions and a feeling of “desperation” drive many to attempt to leave Greece for other states in Europe.
Mr Kanaris argued it was “against human rights” to return asylum seekers after a “perilous and very expensive trip” from Greece and their countries of origin.
The EU’s executive arm recommended in December that the policy of returning asylum seekers be reinstated, and people who arrived in Greece after March 15 before travelling on to other countries are now liable to be returned.
New arrivals continue to land in hotspots like Lesbos although in smaller numbers than 2015, when 800,000 arrived.
Nearly 12,000 migrants have landed in Greece this year compared to 96,000 in Italy, and 2,420 have died attempting to cross the Mediterranean.