Authorities believe the businessman, Yoo Byung-eun, owns the ship and that his alleged corruption may have contributed to the sinking.
As the crew members stood with bowed heads, families of the victims struggled to contain their fury.
Prosecutors asked for a court-issued arrest warrant after billionaire businessman Yoo Byung-Eun failed to heed an official summons.
More than three weeks after the ferry sank, 29 passengers remain missing, 275 bodies recovered so far, most of them high school students.
Bodies were found late on Saturday in the inverted, submerged ship, bringing the confirmed death toll from the April 16 disaster to 275.
15 crew members involved in the ferry’s navigation have been arrested, accused of negligence and failing to protect passengers.
Diver was unable to breathe by himself when he was brought to the surface, and his death was later confirmed at a hospital.
South Korean recovery workers strengthened a ring of netting around a sunken ferry to try to prevent corpses drifting away.
S. Korean President Park Geun met families of ferry victims for the second time as divers recovered two more bodies
Tracking data show the ship made a 45-degree turn around the time it began sinking.
The operation to recover bodies from the ferry that sank off South Korea last month has been suspended due to heavy seas.
Divers have recovered 212 bodies from the wreckage, but 90 passengers are still missing.
The apology came as divers on Tuesday fought strong currents in their search for more than 100 missing passengers.
Prosecutor Yang Jung-jin of the joint investigation team says two helmsmen and two members of the steering crew were detained Saturday.
Officials said on Tuesday that confirmed fatalities had reached 104, with nearly 200 people still missing.