Sixty-four people are known to have died and 238 are missing, presumed dead, in the sinking of the Sewol ferry last Wednesday. Most of the victims are high school children.
Captain Lee Joon-seok, 69, and two other crew members were arrested last week on negligence charges, with prosecutors announcing four further arrests - two first mates, one second mate and a chief engineer - on Monday.
Several crew members, including the captain, left the ferry as it was sinking, ahead of the passengers, witnesses have said.
Park said the crew's desertion was tantamount to murder.
"Above all, the conduct of the captain and some crew members is unfathomable from the viewpoint of common sense, and it was like an act of murder that cannot and should not be tolerated," Yonhap news agency quoted her as saying during a meeting with aides.
Lee, the captain, said in a promotional video four years ago that the journey from the port city of Incheon to the holiday island of Jeju was safe - as long as passengers followed the instructions of the crew.
He also told a newspaper that he had been involved in a sea accident off Japan years before.
The irony of the video is the crew ordered the passengers to stay put in their cabins as the ferry sank. As is customary in hierarchical Korean society, the orders were not questioned.
However, many of those who escaped alive either did not hear or flouted the instructions and were rescued as they jumped off the deck.
Of the 476 passengers and crew on board, 339 were children and teachers on a high school outing.
"Passengers who take our ship to and from Incheon and Jeju can enjoy a safe and pleasant trip and I believe it is safer than any other vehicle as long as they follow the instructions of our crew members," Lee said in the 2010 promotional video, according to transcripts broadcast by regional cable station
The Jeju Today newspaper interviewed Lee in 2004 when he spoke of close shaves at sea including passing through a typhoon and a previous sinking off Japan.
"The first ship I took was a log carrier vessel and it capsized near Okinawa. A helicopter from Japan's Self-Defense Force came and rescued me. Had it not been for their help, I wouldn't be here now."
The newspaper did not give further details.
"I KNOW HOW HE SAID 'DAD'"
Parents of the children missing in the accident in what is likely to turn out to be one of South Korea's worst maritime disasters sat exhausted from days of grief on Monday, waiting for the almost inevitable news that their loved ones had died.
They have spent all their time since the accident in a gymnasium in the port city of Jindo, taking it in turns to vent their anger at the crew's inaction and slow pace of the rescue operation.