The 9.77-tonne Dolphine, believed to have been carrying 21 passengers, capsized near the southwestern island of Chuja Saturday night.
Three were rescued by fishermen after holding on to a floating piece of the boat for more than 10 hours. Ten bodies including the captain's were found on Sunday.
More than 70 coastguard, navy and civilian fishing vessels, supported by helicopters and search aircraft, combed the area around the island on Monday.
Many passengers were not wearing life vests when the boat capsized, local media quoted survivors as saying.
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Officials had vowed to overhaul public safety and toughen penalties for violations. But critics say little has been done.
"Nothing has changed even after the Sewol," ran the front page headline of the Dong-A newspaper.
It accused the coastguard of a slow and insufficient response and criticised the "lack of safety concerns" that led the boat to sail despite bad weather.
"How many deaths do we need to make the government and people set things right?" the newspaper said in an editorial.