The captain initially told passengers to stay in their rooms and waited more than half an hour to issue an evacuation order as the ferry Sewol sank.
By then the ship had tilted so much that many of the roughly 240 people missing are believed to be trapped inside.
Ms Park said the captain and crew “told the passengers to stay put but they themselves became the first to escape, after deserting the passengers”.
She said that “legally and ethically, this is an unimaginable act.
Earlier, four more crew members were detained on allegations of failing to protect passengers.
Senior prosecutor Ahn Sang-don said two first mates, one second mate and a chief engineer are also accused of abandoning the ship.
Prosecutors are considering whether to ask a court for a formal arrest warrant that would allow for a longer period of investigation. South Koreans can only be detained for 48 hours without a court-issued arrest warrant.
The ferry’s captain and two other crew members were previously formally arrested on suspicion of negligence and abandoning people in need.
Sixty-four bodies have been recovered from the vessel.
A radio transcript revealed the ferry was crippled by confusion and indecision well after it began listing.
About 30 minutes after the Sewol began tilting, a crew member asked a marine traffic controller whether passengers would be rescued if they abandoned ship off South Korea’s southern coast. The crew member posed the question three times in succession.
That followed several statements from the ship that people aboard could not move and another in which someone declared that it was “impossible to broadcast” instructions.
Many people followed the captain’s initial order to stay below deck, where it is feared they remain trapped.“Even if it’s impossible to broadcast, please go out and let the passengers wear life jackets and put on more clothing,” an unidentified official at Jindo Vessel Traffic Services Centre urged at 9.24am on Wednesday, 29 minutes after the ferry first reported trouble, according to the transcript released by South Korea’s coast guard.
“If this ferry evacuates passengers, will you be able to rescue them?” the unidentified crew member asked.
“At least make them wear life rings and make them escape” the traffic-centre official responded.
“If this ferry evacuates passengers, will they be rescued right away?” the crew member asked again. “Don’t let them go bare – at least make them wear life rings and make them escape” the traffic official repeated.
“The rescue of human lives from the Sewol ferry ... the captain should make his own decision and evacuate them.”
“I’m not talking about that,” the crew member said. “I asked, if they evacuate now, can they be rescued right away?”
The traffic official then said patrol boats would arrive in 10 minutes, although another civilian ship was already nearby and had told controllers that it would rescue anyone who went overboard.