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Clutching memorial portraits of their children, family members and grieving parents were prevented by riot police from nearing the palace, and instead sat in the middle of the road where they sobbed, wailed and shouted in anger.
"Listen to us, President Park. Just give us ten seconds!," one family member said, using a portable address system. "Why are you blocking the way?," said another. "President Park hear our voices!"
Seated on the ground in the middle of the night, they wore beige blankets and huddled in rows on the cold floor. One mother, overcome with grief, quietly sobbed as she stroked a portrait of her dead son.
Park's government has faced continued criticism for its handling of the disaster from the families of the ferry victims, many of whom believe a faster initial response could have saved many more lives.
South Korean prosecutors are seeking the arrest of members of the family that owns the ferry operator, and may also seek the extradition of a son of the reclusive head of the family from the United States, an official said on Thursday.
The Sewol, overloaded and travelling too fast on a turn, capsized and sank about 20 km (12 miles) off the southwest coast on a routine journey from Incheon on the mainland to the southern holiday island of Jeju, killing hundreds of children and teachers on a high school outing.
Only 172 people have been rescued and the remainder are all presumed to have drowned. An estimated 476 passengers and crew were on board.
However, some of the crew, including the captain were caught on videotape abandoning ship while the children were told numerous times to stay put in their cabins where they awaited further orders.
They paid for their obedience with their lives.
Heartbreaking new video released by families on the march showed students laughing as they tried, and failed, to scramble up a vertical floor.
Earlier footage recovered from the students' mobile phones shows them playing around as the ship started listing, even joking about the sinking of the Titanic, when they had plenty of time to jump overboard.
Only two of the vessel's 46 lifeboats were deployed.
The prosecutors' pursuit of a son and a daughter of Yoo Byung-un, the head of the family that owns Chonghaejin Marine, the ferry operator, broadens the criminal investigation into the tragedy. The government has also started the process of stripping the company of its licence to operate ferries.
It was not clear whether Yoo Byung-un, who ran the defunct commercial empire that was the precursor to the sprawling business interests that include Chonghaejin, might be called in for questioning.
Yoo's son Hyuck-ki, who is believed to be in the United States, has failed three times to respond to a prosecution summons, an official said. Other aides to Yoo are also believed to be abroad and have ignored summonses.
"Since it is an important issue that has drawn public attention, we will do our best (to ensure) their attendance and forcible extradition," said Kim Hoe-jong, second deputy chief prosecutor at Incheon District Prosecution Service.
Prosecutors arrested several officials of the ferry operator and its affiliates, including Chonghaejin's chief executive, on charges of negligence causing death and the sinking of a vessel on Thursday.
All 15 of the surviving crew members, including the 69-year-old captain, have been arrested and face charges of gross negligence amid accusations they abandoned the vessel without performing emergency escape procedures.
Yoo's sons, Yoo Hyuck-ki and Yoo Dae-kyun, are majority owners of Chonghaejin Marine through an investment vehicle.
The prosecution is working with the U.S.' Federal Bureau of Investigation and Department of Homeland Security for possible extradition of Yoo Hyuck-ki, the prosecutor said.
Prosecutors have also raided the shipping company's offices and financial regulators are investigating borrowings of the company and of businesses that are part of a wider holding firm.
Son Byoung-gi, a lawyer who has spoken for the family previously, did not immediately comment.
South Korea, Asia's fourth-largest economy and one of its leading manufacturing and export powerhouses, has developed into one of the world's most technically advanced countries, but faces criticism that regulatory controls have not kept pace.
Nearly 450,000 people have paid tribute to the victims at the altar set up near the school many of the children attended.