A ministry source told AFP new rules would be adopted "in the coming days" to withhold cash subsidies for repatriation from those migrants who appeal against the rejection of their asylum claim.
Organised by the International Organisation for Migration, the repatriation programme has returned some 7,000 people since European states shut their borders to migrants early last year.
Participants are also given 500 euros ($537) as an incentive to return home and to help them with reintegration.
For the time being, those stuck on Greek islands under last year's EU-Turkey migration pact also are given 1,000 euros.
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If they fail to do so, they will no longer be entitled to join the programme -- and lose the cash benefits.
Migration Minister Yiannis Mouzalas on Thursday said thousands of migrants are "abusing" the system by lodging appeals against the rejection of their asylum claims, causing a "bottleneck" in the procedure.
"Whoever lands on Greek soil requests asylum," Mouzalas told reporters.
"There is no other way to help those who really are entitled to asylum and quickly process their claim," he said.
Most of them have filed for asylum to avoid being sent back to Turkey, but these applications take months to handle. Humanitarian groups have repeatedly sounded the alarm over declining morale in their camps.
On Thursday, a Syrian man was badly hurt after setting himself on fire at a migrant camp on the island of Chios. A policeman who tried to stop him was also hurt.