Human Rights Watch and Amnesty International challenge charges against 24 volunteers, who had gone on trial accused of smuggling-related charges.
"This systematic practice endangers the life of people, including young children, that often end up abandoned in the middle of the sea," refugee rights groups say in a letter to Pope Francis ahead of his visit to Greece.
Greece says it will reject the majority of refugees coming via Turkey despite EU laws requiring European nations to share the responsibility of asylum seekers.
The lawsuit at the European Court of Human Rights says Athens carried out a violent and massive coordinated operation against 200 people stranded on a boat.
Refugees can only seek asylum in the country they first entered on arrival in Europe, but a German court is challenging this with a ruling that may offer hope to Syrians facing deportation.
Former Greek international goalkeeper Antonios Nikopolidis has helped start a football team that brings together refugees from Syria, Yemen, Iraq and Afghanistan.
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