"This [escape] was an insult which I will not accept... I will take measures as harsh as necessary,'' Nikos Dendias, Greece's justice minister said.
The pilot was later discovered bound and gagged, claiming he was abducted by an armed couple and forced into helping the two prisoners escape.
The escape came just days before Paleokostas and Rizai were due to stand trial for a similar breakout in 2006, when a hijacked helicopter landed in the jail's central courtyard.
Guards failed to avert the incident, believing the aircraft's arrival was part of a visit by prison officials.
Paleokostas, who is in his forties, was serving a 25-year sentence for kidnapping and bank robbery and awaiting trial at the time of the escape.
Rizai, an Albanian in his thirties, was serving a life term for murder, and has since also been charged over two contract killings while on the run from the June 2006 escape.
Security is being tightened around Paleokostas' brother Nikos, who masterminded the 2006 escape and is currently in prison.
Korydallos holds some of the country's most notorious criminals, including the leaders of the organisation, November 17, who were found guilty of murdering politicians, businessmen and foreign diplomats.