The Seonchang-1 fishing boat was carrying 20 passengers on a fishing tour as well as two sailors when it crashed with the 336-tonne fuel tanker at around 6 am (2100 GMT) at sea near the port city of Incheon.
Thirteen people were found dead or died after being sent to hospitals. Seven others were being treated at hospitals while two -- including the captain of the boat -- remained missing, according to the coastguard.
No casualties or injuries were reported among those on board the tanker.
TV footage showed the fishing boat sinking beneath churning waves while rescue divers searched around the deck, part of which was still visible above the water.
Deadly accidents involving fishing tour boats often make headlines in the South.
Sunday's accident was the worst since September 2015 when 15 died after a fishing tour boat capsized near the southern resort island of Jeju.
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