Dozens of parents of high school students killed in South Korea's ferry disaster camped out near the presidential Blue House in Seoul on Friday, demanding a meeting with President Park Geun-Hye.

Holding portraits of their children who perished when the Sewol ferry sank with the loss of around 300 lives last month, they staged a sit-in at a street corner, a few hundred metres from the Blue House.

A heavy police presence, including officers in riot gear, prevented them moving any closer.

"We're calling for a meeting with the president to press our demands", a spokesman for the families, Kim Byeong-Kwon, told AFP.

The victims' relatives have been extremely critical of nearly every aspect of the government's handling of the disaster.

They want explanations for perceived delays in the initial rescue effort, and for those responsible to be punished.

They also want more resources deployed at the recovery site to speed up the retrieval of the bodies of around 30 passengers still unaccounted for.

Supporters of the group pasted small, yellow paper boats on the sides of police vehicles with handwritten messages reading "I'm so sorry, children", "Remember the Sewol" and "Shame on South Korea".

A few representatives of the families were later allowed into the Blue House for talks with a top presidential adviser for political affairs.

The demonstration began late Thursday night as a protest focused on state-funded KBS TV for commenting that the death toll from the Sewol was far lower than the number of those killed every year on South Korea's roads.

The parents then decided to march to the Blue House to demand a meeting with Park.

The Sewol was carrying 476 people when it sank on April 16 after listing sharply to one side and then rolling over.

Of those on board, 325 were children from a high school on an organised trip to the southern resort island of Jeju.

Initial investigations suggest the ferry was carrying up to three times its safe cargo capacity.

Many parents believe some children may have survived for hours or even days inside airpockets in the capsized ferry, but died because rescuers took too long to access the submerged vessel.

Kim Hyeon-Dong said the condition of his daughter's body -- recovered six days after the sinking -- suggested she was alive for part of that time.

"Her body wasn't decomposed at all. I believe she must have stayed alive for quite a long time after the boat rolled over", he said.

"What we are especially angry about is the fact that many of our children would have made it if help had come earlier", he said.

The confirmed death toll stood at 273 on Friday, with 31 still unaccounted for, after four more bodies were retrieved from the sunken ship overnight.