A special court on Monday rejected the petition of three imprisoned Golden Dawn members that were seeking release.
The five-member sentence-suspension court said the three would remain in jail pending the final appeal of their case.
The head of the Golden Dawn branch in Perama, Anastassios Pantazis, was convicted for being a member of a criminal organisation and for participating in an attack against Egyptian fishermen at Ikonio in Perama, a western neighbourhood of Piraeus.
His 12-year conviction also included participation in an attack against Communist Party labour union PAME outside the ship repair area of Perama.
The chief magistrate in the court recommended the rejection of Pantazis' petition because the party he claims is disbanded is actually still active "but with covered-up activities."
The crimes for which he was convicted "relate to a long-term history and the applicant took part in more than one incidents. If released, he will be on suspicion of carrying out new felonies," Niki-Anastasia Mouzaki said.
She added that the health problems that the Golden Dawn member is citing are not so serious they cannot be dealt with, nor do they carry the risk of irreversible damage.
Anastassios Anadiotis, who was served a 7-year sentence for participating in the murder of rapper Pavlos Fyssas and membership in a criminal organization, said he wanted to attend a graduate studies program he was accepted in. His release was rejected.
Aristotelis Chryssafitis, who had also been convicted with 7 years for the same charges as Anadiotis, had his petition rejected as groundless.
This past week the court approved a petition by the Nikea branch leader Giorgos Patelis, whose sentence was suspended and he was released on restrictions.
Patelis appealed on the grounds of irreparable damage to his child's health.
The Greek Supreme Court will review the decision, by order of the chief prosecutor Vassilis Plotas.