They also sought life sentences for three senior crew members and prison terms of between 15-30 years for 11 others as the trial of Captain Lee Joon-Seok and his crew wound up in the southern city of Gwangju.
The 69-year-old Lee "escaped the ship without making any efforts to rescue passengers", the prosecution team said in its sentencing recommendation to the court.
"He made excuses and lied. He showed no repentance... And so we ask for the death sentence," the prosecution said.
The disaster was blamed on a deadly combination of cargo overloading, illegal redesign and poor helmsmanship, but the most serious charges against Lee and his crew related to their response once the ship ran into trouble.
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They were among the first to climb into rescue boats and were publicly vilified for abandoning the hundreds of passengers still trapped inside.
Crew members were further condemned when it emerged they had instructed the passengers to remain where they were as the vessel began to list dangerously -- a decision which the prosecution said contributed to the heavy loss of life.
The court is expected to deliver its verdict and sentence in early November.
Although the death penalty is still passed in South Korea, nobody has been executed since 1997. Currently, there are some 60 people on death row.
Lee has insisted that the ferry owners are the real culprits as it was their decision to consistently overload the vessel and commission an illegal redesign.
South Korean media coverage of their arrest and arraignment was often coloured by a presumption of guilt, and just weeks after the disaster President Park Geun-Hye stated that the crew's actions had been "tantamount to murder".