Prime Minister Chung Hong-won resigned on Sunday saying that staying in his post was “too great a burden on the administration”.
“On behalf of the government, I apologise for many problems from the prevention of the accident to the early handling of the disaster,” he said.
“There are too many irregularities and malpractices in parts of society that have been with us too long and I hope those are corrected so that accidents like this will not happen again.”
The resignation needs to be accepted by South Korea’s president.
In the early stages of the crisis, the government announced that everyone had been rescued from the ferry. The confirmed death toll from the 16 April disaster now stands at 187 – and is expected to rise.
Many of those missing or dead were students and teachers from the Danwon high school on the outskirts of Seoul, who were on a field trip.
The Gyeonggi Provincial Office of Education sent text messages to parents that “All Danwon High School students are rescued” in the hours after the disaster, media reported.
The Sewol ferry, carrying 476 passengers, sank on a routine trip from the port of Incheon, near Seoul, to the southern holiday island of Jeju – near the city of Jindo.
One Jindo resident said on Sunday: “The rescue operation was too tardy to save the people, and I felt as if my own children were drowning. I cried a lot.”
Yellow ribbons have been hung along the seafront at Jindo, where many family members are wiating to hear news.
Meanwhile, divers in the seas near the site where the ferry sank have failed to find any bodies for more than 24 hours as bad weather turns conditions challenging.
South Korean coast guard spokesman Ko Myung-suk said on Sunday: “A preliminary high seas watch has been issued since 4am, yesterday and we’re expecting worse weather conditions today. The search operation is expected to face more difficulties today.”
Investigations into the cause of the tragedy are focused on human error and mechanical failure.