They also charge police have stopped people based only on their appearance, ekathimerini.com reported.
The operation, given the name Xenios Zeus from the Greek word for foreigner and the leading god in the classical pantheon, began last weekend. More than 6,000 people were stopped, questioned and searched, and 1,400 were detained.
The Greek Council of Refugees said Thursday the country has a right to control its borders but also has an obligation to respect the human rights of people with genuine fear of persecution in their homelands.
Greece, because of its geographical position, has become a gateway for Africans and Asians trying to get into Europe. Public Order Minister Nikos Dendias said Thursday there are no plans to stop the crackdown on undocumented immigrants and met with Prime Minister Antonis Samaras to discuss it.
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