SEOUL, South Korea — President Park Geun-hye of South Korea vowed on Monday to disband her country’s Coast Guard, saying that South Korea owed “reform and a great transformation” to hundreds of high school students who died in a ferry disaster last month.

Bowing deeply, Ms. Park offered a “heartfelt apology” for having failed to prevent the sinking of the ferry Sewol on April 16 and for the Coast Guard’s bungling of rescue operations.

“The ultimate responsibility lies with me, the president,” she said.

Although she had apologized a few times over the sinking, Ms. Park’s nationally televised speech on Monday was her clearest expression of public contrition. As of Monday, 286 people had been confirmed dead, with 18 missing, making the episode one of the country’s worst peacetime disasters. It has also developed into Ms. Park’s biggest political crisis; over the weekend, the police detained more than 200 people who had tried to march on her office, calling on her to step down.

“We failed to save those students who should have been saved,” Ms. Park said. “I will make this an opportunity for South Korea to be born again.”