Chung Hong-won’s resignation comes amid rising indignation over claims by the victims’ relatives that the government did not do enough to rescue or protect their loved ones. Most of the dead and missing were high school students on a school trip.
A spokesman said President Park Geun-hye would accept the resignation, but did not say when Mr Chung would leave office.
Officials have arrested all 15 people involved in navigating the ferry Sewol, which sank on April 16.
A prosecutor revealed that investigators were also looking into communications made as the ship sank between a crew member and the company that owns the ferry.
Mr Chung was heckled by victims’ relatives and his car was blocked when he visited a shelter on an island near the site of the sinking a week ago. Yesterday, he gave his reasoning for the resignation to reporters in Seoul.
“As I saw grieving families suffering with the pain of losing their loved ones and the sadness and resentment of the public, I thought I should take all responsibility as prime minister,” Mr Chung said.
“There have been so many varieties of irregularities that have continued in every corner of our society and practices that have gone wrong. I hope these deep-rooted evils get corrected this time and this kind of accident never happens again.”
Meanwhile, senior prosecutor Yang Jung-jin said that two helmsmen and two members of the steering crew who were detained on Saturday had been formally arrested. Eleven other crew members, including the captain, had been arrested earlier.
Mr Yang also said that a crew member called the ship’s owner, Chonghaejin Marine, as the ferry was listing April 16, but declined to disclose whether the caller was the captain.
Media said the captain called for company approval of an evacuation. Prosecutors said they are analysing the content of communications between the ship and the company.
The arrested crew members are accused of negligence and of failing to help passengers in need. The captain initially told passengers to stay in their rooms and took half an hour to issue an evacuation order, by which time the ship was tilting too severely for many people to get out.
Divers have recovered 188 bodies and 114 people are believed to be missing, although the government-wide emergency task force has said the ship’s passengers list could be inaccurate. Only 174 people survived, including 22 of the 29 crew members.
The seven surviving crew members who have not been arrested or detained held non-marine jobs such as chef or steward, according to Mr Yang.
Captain Lee Joon-seok told reporters after his arrest that he withheld the evacuation order because rescuers had yet to arrive and he feared for passengers’ safety in the water. Helmsman Oh Yong-seok, one of those arrested on Saturday, has said he and several crew members did their best to save people.
He said he and four crew members worked from nearby boats to smash windows on the ferry, dragging six passengers stuck in cabins to safety.
A Spanish ferry carrying 334 people in the Canary Islands had to return to port when a fire broke out on one of its car decks, forcing an evacuation of the vessel. No one was injured.