EU and Greek officials on Thursday said 5,000 asylum seekers on Greek islands would be given financial incentives to return home to relieve pressure on overwhelmed camps.
The plan, available for a month only and based on a 2,000-euro stipend, is only open to those who arrived in Greece before January 1.
"We have now agreed on a special temporary assisted voluntary return scheme...for a period of one month," EU home affairs commissioner Ylva Johansson said after talks in Athens.
"We think it will be an open opportunity for 5,000 migrants," she said.
The money is designed to help asylum-seekers start afresh in their countries of origin, she said.
"It's clear that we are facing a national emergency and we need to protect our borders," said Greek migration minister Notis Mitarachi.
Voluntary returns would be carried out with help from the International Organisation for Migration and EU border agency Frontex.
The offer does not apply to refugees who arrived during a two-week surge enabled by Turkey, which said on February 28 that it would no longer prevent people from trying to reach the European Union.
As a result of the surge -- which has been accompanied by skirmishes at the border between migrants and Greek and Turkish riot police -- Greece has announced it will not accept new asylum applications until April.
Hundreds of people have arrived by sea on Greek islands near Turkey where there are already more than 37,000 asylum seekers in camps originally built to house around 6,000.
Lacking space, Greek authorities have put over 450 migrants on a navy ship docked at the Lesbos port of Mytilene, where conditions are already described as poor.
In May, Greece is to host a conference on the hundreds of unaccompanied minors who are most at risk among asylum seekers, Johansson said.
Seven EU states have already pledged to take at least 1,600 unaccompanied minors and children, she added.
"We are not well-prepared enough. We are still lacking a common policy for European migration and asylum," Johansson said, adding that she would present proposals next month.
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