South Korea's prime minister has announced his resignation over the widespread criticism over the government's response to the April 16 ferry disaster.

Prime Minister Chung Hong-won announced his resignation early on Sunday at an emergency news conference in Seoul, the capital.

"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."

Chung's resignation was approved by President Park Geun-hye although her spokesman later said that he would remain in his post until the rescue operation was completed, the Reuters news agency reported.

The Sewol ferry sank on a routine trip south from the port of Incheon to the traditional holiday island of Jeju.

The Sewol ferry sank in waters off Jindo Island in the southwestern province of South Jeolla on 16 April [EPA]

The government, along with almost all of its branches, has come under fierce criticism over the disaster, and the handing of the rescue operation.

Chung said that he wanted to resign earlier, but had given the situation "first priority," adding that he did not want to be "any burden to the administration".

More than 300 people, most of them students and teachers from one high school on a field trip, have died or are missing and presumed dead.

The children were told to stay put in their cabins, where they waited for further orders. The confirmed death toll on Sunday was 187.

All 15 surviving crew members responsible for sailing the vessel are now in custody and face charges ranging from criminal negligence to abandoning passengers.

Tempers have frayed over the slow pace of the recovery and frequent changes in information provided by the government.

President Park Geun-hye, who has the most power in government, was booed by some of the relatives of the missing when she visited a gym where families of the missing were staying.