The captain of a South Korean ferry that sank on Wednesday leaving hundreds missing, feared dead has been arrested, the country's Yonhap news agency says. Warrants for the arrest of two other crew members have also been lodged with a court.

The arrest came as speculation mounted that more lives could have been saved had the captain, Lee Joon-seok, issued an evacuation order sooner. Investigators were also examining reports that the ferry took a sharp turn just before it started listing as well as claims that Lee, 69, abandoned the ship, as hopes dimmed for the 268 passengers still trapped inside the vessel.

The official death toll from the disaster, which occurred off the south-west coast of South Korea, rose to 29 after several bodies were retrieved from the sea near the wreck of the Sewol.

As hundreds of divers, rescue boats and aircraft continued the frantic search for survivors in difficult conditions about 25km off Jindo, accident investigators focused on the actions of Lee and his crew.

Officials said a junior officer was steering the ship when the ferry capsized, adding that Lee, who has been criticised for apparently jumping into a rescue boat while hundreds of his passengers remained on board, may have been in another part of the vessel. Some reports said he returned to the bridge as soon as the ferry started listing.

"[The captain] may have been off the bridge," Park Jae-eok, an investigating official, told reporters. "And the person at the helm at the time was the third officer."

An image said to show Lee Joon-seok being helped off the stricken ferry. Photograph: Getty Images

Lee, who was being questioned by police about his actions, has come under fire for apparently abandoning the ship 30 to 40 minutes after it began listing. A picture has been released apparently showing him leaving the ship, with the help of maritime police.

Lee has not commented publicly on the situation on the bridge at the time of the accident. On Thursday, he issued a brief apology to the relatives of the dead and missing: "I am really sorry and deeply ashamed. I don't know what to say."

It emerged on Friday that the crew had not acted immediately on an order by a local transportation office to tell passengers to put on life jackets and prepare to evacuate.

The order from officials on Jeju, the ferry's destination, came five minutes after the accident, but the crew did not tell passengers to leave the vessel for at least another 25 minutes. Some survivors said they did not hear any instructions to abandon the ship.

Twenty of the ship's 30 crew survived, reports said.

The ferry was carrying 475 passengers and crew on a trip from the western port of Incheon to the southern resort island of Jeju. The passengers included 325 teenagers and 15 teachers from Danwon high school.

Reports said Kang Min-gyu, the deputy headmaster of Danwon high school, has been found dead in an apparent suicide near a gymnasium on Jindo, an island near the accident site from where the rescue operation is being directed.

A colleague at the school said Kang, who was among 179 rescued passengers, had been overcome with guilt. "As the teacher responsible for the students' safety, he was suffering with serious feelings of guilt," the Korea Herald quoted the teacher as saying. "The families of the victims vented their anger towards him – he was brokenhearted."

The 6,835-ton ferry sank about two hours after issuing a distress signal shortly before 9am on Wednesday. It is still unclear what caused the Sewol to roll on to its side and sink, but there is speculation that it either hit a submerged rock, or began to list after a sharp turn caused poorly secured cargo to shift suddenly to one side of the ship.

Coastguard officials said investigators were looking into possible negligence by the crew and potential problems with the way the cargo was stowed, although the ship reportedly passed all its safety and insurance checks.

Park, the official involved in the investigation, said Lee had turned the controls of the ship over to a 26-year-old third mate with one year's experience. "Although surviving crew members have given different accounts about the situation, we are investigating the captain as he is suspected of leaving the steering room for an unknown reason," the Korea Times quoted Park as saying.

But parents who spent another sleepless night at a hospital in Mokpo, a city close to the rescue operation, were scathing about Lee's actions. "How could he tell those young kids to stay there and jump from the sinking ship himself?" said Ham Young-ho, whose grandchild, 17-year-old Lee Da-woon, is among the dead.

The investigation is also focusing on the the ship's owner, Chonghaejin Marine, in Incheon. The firm added more cabin rooms to three floors after it bought the ferry on 2012, an official at the Korean Register of Shipping told the Associated Press.

The extension work increased the Sewol's weight by 187 tons and created space for another 117 passengers, although experts said such modifications were not unusual.

About 600 divers involved in the rescue operation have been frustrated by strong currents and poor visibility. They were unable to enter the ship after managing to open the door to the ferry's cargo hold, according to South Korea's security ministry. Earlier, the ministry had incorrectly stated that divers were inside the cargo area.

"We cannot even see the ship's white colour. Our people are just touching the hull with their hands," Kim Chun-il, a diver from Undine Marine Industries, told relatives of the missing.

The chances of finding survivors looked increasingly slim on Friday when the ship disappeared completely beneath the water at around noon. Experts have said that people can survive for around 72 hours if air pockets have formed in the ship's compartments; more than 48 hours have passed since the ship capsized.

Divers began pumping air into the ship on Friday, but it was not immediately clear if the air was for possible survivors or to assist the salvage operation. About 170 vessels and 29 aircraft are now involved in the rescue operation, according to the South Korean coastguard. Confronted with its worst ferry disaster for more than 20 years, South Korea has gone into mourning. TV stations took primetime soap operas and variety shows off the air and instead showed documentaries and around-the-clock coverage of the rescue operation.

Companies cancelled social events, while local governments called off festivals, concerts and other events. The country's pop stars abandoned plans to release new albums and postponed concerts and promotional events.

• This article was updated at 9.18pm BST to take in the arrest of the ferry's captain