An official from the Korea Coast Guard said the number of deaths could grow as six among the 13 rescued were unconscious and in critical condition.
He said 22 people were aboard the 9.8-tonne fishing boat that capsized after colliding with the 336-tonne refuelling vessel in waters off the port city of Incheon.
The official spoke on condition of anonymity, citing office rules.
The refuelling vessel did not suffer damage.
President Moon Jae-in ordered authorities to deploy as many helicopters and other aircraft as possible to search for the missing, according to his office.
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