Additionally it is urging EU States to recognise the validity of claims by Eritrean refugees and asylum seekers and to ensure that the principle of non-refoulement is respected.
It claims the human rights record of Eritrea remains one of the most appalling in the world and that the UN Special Rapporteur on human rights in Eritrea, Sheila Keetharuth, has said that Eritrean refugees "are fleeing a country ruled not by law, but by fear.
"They deserve international protection."
Stuart Windsor, from CSW and says Eriterian Christians are under threat: "Thousands have been fleeing the country into Sudan, into Egypt, and into Ethopia and even into Israel.
"And unfortunately they're not always treated correctly and the big issue is that these countries are saying they're not refugees, they are economic migrants and sending them back and some have been executed when they return to Eriteria because they've fled the country or fled the military."
Commenting on the global day, CSW's Chief Executive Mervyn Thomas said, "On World Refugee Day, we remember the millions of people around the world who are displaced from their homes by conflict, violence and persecution, often risking their lives to reach safety either overland or in unseaworthy vessels.
"Violations of freedom of religion and belief are one of the key reasons why people are forced to leave their country.
"We encourage states to strengthen their joint responses to the global refugee crisis and to establish human rights based migration responses where the dignity and safety of migrants remain at the forefront of the efforts.
"EU States especially have a responsibility to recognise the validity of claims by Eritrean refugees and asylum seekers and to ensure that refugees are not returned to any countries where their lives are endangered.
"Above all, we call for compassion towards refugees, cherishing the human dignity of each and every person."
Listen to Premier's Dave Rose speak to Stuart Windsor and Kiri Kankhwende from CSW here: