Chung Hong-Won admitted he had not been up to the task of overseeing rescue operations after the Sewol capsized with 476 people -- many of them schoolchildren -- on board.
"I offer my apology for having been unable to prevent this accident from happening and unable to properly respond to it afterwards," he said.
"I believed I, as the prime minister, certainly had to take responsibility and resign."
There has also been rage over perceived corruption and lax safety standards that may have led to the disaster, with claims that the ferry was overloaded and the passenger list was inaccurate and incomplete.
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"The latest accident left all South Koreans in great shock and sorrow. (Many) days have passed since the accident, but the screams of families of the missing still keep me up at night," Chung told a nationally-televised press conference.
The confirmed death toll from the tragedy stood today at 187, with 115 unaccounted for, their bodies believed trapped in the sunken vessel.
Divers were battling decompression sickness and atrocious weather in their grim search for corpses.
Further complicating their efforts was the increasing depth of the wreck as it sinks slowly into the silt of the seabed, making an already dangerous diving operation even more hazardous.