Updated

South Korean prosecutors are seeking to formally arrest the head of the company that owns a doomed ferry in part of their investigation into its sinking last month that left more than 300 people, mostly high school students, dead or missing, officials said Friday.

Prosecutors asked a court late Thursday to issue an arrest warrant for Kim Han-sik, president of Chonghaejin Marine Co. Ltd, over allegations of cargo overloading, according to a judge at the court in the southern port city of Mokpo.

The Mokpo court will review the request Friday to determine whether to approve Kim's arrest, the judge said on condition of anonymity, citing department rules.

Authorities believe improper stowage and overloading of cargo are one possible reason the ferry sank on April 16. Four employees at Chonghaejin Marine Co. Ltd, who handled cargo on the Sewol, have already been arrested, and Kim faced allegations that he was aware that the ferry exceeded its cargo limit but didn't do anything before it started it trip, senior prosecutor Yang Jung-jin said. Kim was detained on Thursday.

"I feel very sorry for the victims .... their family members. I committed a grave sin," Kim, wearing a cap and a mask, told reporters at a detention facility in Mokpo, according to South Korean TV footage. He declined to comment on questions over alleged cargo overloading.

More than three weeks after the sinking, 273 bodies have been retrieved but 31 others are still listed as missing. Searches have been hampered by strong currents, bad weather and floating debris inside the ship. A civilian diver fell unconscious while searching and died on Tuesday.

Relatives of the dead and missing passengers and many other South Koreans have been highly critical of the government's handling of the rescue effort, and the regulatory failures that may have allowed the disaster to happen.

Family members marched to the presidential Blue House in Seoul early Friday calling for a meeting with President Park Geun-hye but ended up sitting on streets near the presidential palace after police officers blocked them. Park's office said a senior presidential official plans to meet them later Friday. No violence was reported.

Park has apologized over the sinking at least three times but her apologies came during meetings with top officials, religious leaders or in a speech marking Buddha's Birthday holiday. Family members and critics say Park should deliver a special speech on the sinking to the whole nation.

All 15 surviving crew members involved in the ferry's navigation have been arrested, accused of negligence and failing to protect passengers. Besides possible freight problems, prosecutors say they are looking into other factors, such as the turn made during the time the ship began listing, ocean currents and modifications made to the ship.