"Crisis-hit Greece alone cannot support the weight of accommodating war refugees," said Nander Halbuni, a representative of the Syrians who have been camping on Syntagma Square in central Athens for over a week.
"The only solution for ourselves and our families is to have the right to go to another (European) country to start a new life of dignity for our children," he told reporters.
The Syrians began their protest on November 19 to demand housing from the Greek authorities, after spending months sleeping in parks or in the street.
More than a dozen have mounted a hunger strike and have been been hospitalised after fainting.
Greece is one of the main points of entry into the European Union for people fleeing war-torn and poor countries in Africa, the Middle East and the Indian sub-continent.
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Many of the recent arrivals are escaping the war in Syria, where more than 200,000 people have been killed, according to UN figures.
Some 28,000 Syrians have been caught illegally entering Greece since January, compared to just 8,500 last year.
Also Friday, authorities on the island of Crete completed the disembarkation of nearly 600 migrants rescued from a freighter flagged in the Pacific island of Kiribati.
The migrants -- which include 150 women and children -- will be temporarily housed in an indoor sports hall in the coastal town of Ierapetra.
Eleven of the migrants have been hospitalised.
Seven crew members of the freighter Baris were being questioned on suspicion of migrant smuggling.