An image of some of the 92 men found naked and bruised on the Greek-Turkish border was tweeted by Greece's migration minister.
EU border agency Frontex confirmed to AFP the arrival of the group in circumstances which the Greek ministry for civil protection said sent out an "inhuman image."
"The Frontex officers reported that the migrants were found almost naked and some of them with visible injuries," said Paulina Bakula, spokeswoman for the organisation.
Bakula, speaking from Frontex's Warsaw HQ, said Frontex officers worked with Greek authorities to provide the migrants -- mainly Afghans and Syrians -- with immediate assistance.
She added the organisation had informed the agency's fundamental rights officer of a potential rights violation.
Greek minister for civil protection, Takis Theodorikakos, accused Turkey of "instrumentalising illegal immigration" in the latest of a series of recriminations on migration between the neighbours.
Theodorikakos told Skai television many of the migrants had told Frontex that "three Turkish army vehicles had transferred them" to the river which acts as a natural border.
Ankara denied any responsibility and Interior Minister Ismail Catakli called on Greece to stop what in a tweet he termed its "manipulations and dishonesty."
Greek minister for migration and asylum, Notis Mitarachi, had Saturday described the incident as a "shame on civilisation."