Park's apology comes amid public criticism and grief over the disaster
South Korean President Park Geun-hye has apologised over the ferry disaster, in a statement to cabinet shown on national television.
Park said that the government had failed to prevent the disaster and bungled its emergency response.
Her apology comes amid ongoing work to retrieve bodies from the sunken hull.
The ferry sank with 476 people aboard - most of them high school students and teachers - off South Korea on 16 April. A total of 174 were rescued.
The remainder has been confirmed dead or missing presumed drowned.
Officials have retrieved almost 200 bodies and divers are continuing to search for those still unaccounted for.
"I don't know how to apologise for the failure to prevent this accident, and for the insufficient first response," Park said in the statement.
"I am sorry to the people and heavy-hearted that many precious lives were lost."
Park's apology comes amid mounting public anger and criticism over the disaster. Most of those on board were on a trip from Danwon high school in Ansan, south of Seoul.
President Park had earlier paid her respects at a memorial altar set up near the school. Local media reports said she was heckled by angry family members.
Attention has focused on why so few people were evacuated from the stricken vessel, and on the possibly negligence of the captain and crew.
On Sunday, South Korean Prime Minister Chung Hong-won offered his resignation over the disaster.
In her statement, Park she would create a new government agency to handle large-scale accidents, Yonhap news agency reported.
The national safety ministry would also be placed under the prime minister's office, the agency said.
"We should have a firm determination to make the entire safety system from scratch," Park said.
"The entire Cabinet should come up with safety measures for the people with an attitude to remodel the country from square one."
It is not yet clear what caused the incident but investigations are focusing on whether modifications made to the vessel made it more unstable.
Reports have emerged that the sleeping cabins were refitted some time between 2012 and 2013, which experts say may have inadvertently affected the balance of the vessel.
The ferry was also reported to be carrying cargo more than three times its approved amount.
All 15 crew members involved in the navigation of the ferry are now in custody, facing criminal negligence charges.
New pictures emerged on Monday that showed ferry captain Lee Joon-seok, 69, wearing a sweater and underpants, being rescued from the tilting vessel.
He was not at the helm when the ship got into trouble - instead the vessel was being steered by a third mate.
Another focus of the investigation is why passengers were told to remain in their cabins as the ship listed.
Divers have found many bodies of passengers, wearing life jackets, in cabins and public areas inside the ship.