South Korean President Park Geun-Hye on Thursday faced the angry parents of hundreds of children missing in a ferry disaster, holding an impromptu and at times very tense meeting in an island gymnasium.

Park's security detail looked decidedly nervous as emotions boiled over, with distraught parents screaming at the president and other officials standing with her on a stage in the auditorium in Jindo island.

"What are you doing when people are dying! Time is running out!" one woman shouted as Park tried to speak.

Clearly moved by the despair of the relatives, Park found herself in an unusually vulnerable position for any head of state, engaging in a lengthy question and answer session with a volatile crowd.

Much of the anger was focused on the head of the South Korean coastguard, Kim Suk-Kyoon, with relatives insisting not enough was being done to find survivors more than 30 hours after the ferry sank on Wednesday morning.

When Kim countered that there were 550 divers involved in the search effort, he was immediately drowned out by jeering and booing, with one furious parent shouting: "But none of them are actually in the water!"

Park tried to calm the mood down, and promised that no effort would be spared in the rescue and recovery process.

"You must be so worried, unable to sleep at all last night," she said. "Never lose hope and please wait for the news of rescue."

But some parents responded by shouting they were being kept out of the loop, and only being fed scraps of information.

"I think we should make more efforts to make sure that families know every single detail of what's going on," Park said, turning to the other officials and drawing applauses from the crowd.

"This is a matter of trust with the relatives. We will do our best to rescue the last single person," Park added.

Earlier, the president had taken a boat to the rescue site where she urged divers to press on, despite the exceedingly dangerous conditions, with strong currents and almost zero visibility.

"Time is running out. Please hurry," she told the members of one dive team. "If there are survivors, every minute and second is critical."