The coast guard said the accident happened west of Jeju island. Local authorities said 12 crew members had been on board - six South Koreans and six Vietnamese nationals.
Train inferno: 13 passengers from Mirpurkhas remain missing
Only one body - the badly burned corpse of a South Korean - had so far been recovered, a coast guard official told AFP.
Helicopters, a patrol plane, coast guard vessels and civilian fishing boats were involved in the search for the missing, the coast guard said, adding that the cause of the fire was under investigation.
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