Jindo, South Korea (CNN) -- South Korea's prime minister announced his resignation Sunday morning, taking responsibility for the slow initial reaction to a ferry's sinking that has left nearly 200 dead and scores more still missing.

Prime Minister Chung Hong-won explained his decision on national television. He apologized "on behalf of the government for the many problems that arose during the first response and the subsequent rescue operation," in addition to "problems that existed before the accident."

"During the search process, the government took inadequate measures and disappointed the public," Chung said. "I should take responsibility for everything as the prime minister, but the government can assume no more. So I will resign as prime minister."

Chung urged South Koreans to stand united, rather than divided.

"This is not the time for blaming each other but for finishing the rescue operation and dealing with the accident," he said. "In order to get over these difficult times, I ask the citizens for help." 

Chung becomes the highest-profile public figure to fall after the April 16 capsizing of the Sewol ferry that carried more than 300 South Korean high school students. Many in the country have lambasted the government's response to the disaster. Searchers continue to still look for passengers and crew, and so far have retrieved 188 bodies. Another 114 people are still missing.

A father of a missing ferry passenger -- a girl -- called Chung's resignation "meaningless."

He and the girl's mother and sister are outraged at the government about what they say is a disorganized rescue operation.

Chung "doesn't want to take responsibility for this mess," the mother told CNN's Nic Robertson.

She felt that if President Park Geun-hye were to resign "that might actually do something."

The prime minister's role is to coordinate other ministries within government, say experts in South Korean politics. The president appoints the prime minister, and Park will choose the next prime minister.

Though the legislature can question that person before he or she takes the job, ultimately the president alone has the power to choose who gets the job, said Nicholas N. Eberstadtwith the American Enterprise Institute, who has written extensively about North and South Korea.

Chung wasn't "a beloved figure, but he wasn't especially unpopular," Eberstadt said.

The capsizing of the ferry is the biggest disaster in recent South Korean history, and it's a huge story there, occupying hours and hours of news coverage, said David Straub, the associate director of the Korean Studies Program at the Walter H. Shorenstein Asia-Pacific Research Center at Stanford University.

Park is very popular, he said. 

"I'm sure she and the people around her are concerned about (how the ferry disaster has unfolded)," Straub said.

Both experts said they thought it was inconceivable that the president would resign.

A single body

South Korea's joint task force in charge of the search and rescue mission told CNN on Sunday that a closed-door meeting between rescuers and families was held to discuss possible new search tactics.

Rescuers explained that divers are having difficulty trying to reach the Sewol ferry floors close to the seabed, so officials are considering two options. They might use a special metal tool to cut through steel and other materials, or use small explosives to break down the wall. But the second option brings risk that some of the bodies could be damaged.

CNN is trying to get obtain reaction from the task force and the families to this meeting.

The talk comes 11 days after the ferry capsized. The search Sunday was suspended due to bad weather that made diving through the murky waters especially dangerous, but divers made an exception and went down to recover a single body.

A day earlier, divers found the bodies of 48 girls -- wearing their life jackets -- pressed into a room too small for so many people.

Divers believe that they will face the same scene again. There may be a second, similar room, where 50 more girls are believed to have been trapped when the ferry rolled over.

South Korean coast guard diver Kim Dong-soo said he had tears in his eyes when he heard about the accident.

"Even now, I'm searching as if I'm looking for my own children -- and other coast guards feel the same way," he told CNN. "I have two medical patches on me, have difficulty breathing and my head hurts. But it hurts the most in my heart, knowing those children are still in the cold water."

Those still diving face a search that is getting harder and slower.

Now they will head down deep for cabins near the seabed.

In the cramped spaces, divers have been battling a forest of drifting objects and doors forced shut by tremendous water pressure. Currents tug at the breathing tubes that keep them alive as they look for the dead.

There may be fewer bodies to retrieve, but divers have already searched the easily accessible places, said South Korean navy Capt. Kim Jin-hwang, commander of the rescue operation.

"But the navy will not stop until the last body is found," he said 

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This is so sad.. I can't even imagine the emotions of the parents and families atm. 

But I agree with the people. The PM resigning doesn't make any difference. It just makes him look like he doesn't want to deal with anything. Now if the president resign, I dunno about that one. 

I wish I was in Korea to help, even thought I can't swim worth a >< 

#PrayForSouthKorea