"We're doing our best to remove the contamination as quickly as possible, but it will take some time to clean up the shore because it needs to be done by hand," said Kim Woon-tae, a coast guard official.
Coast guards said they were attempting to prevent the slick damaging nearby marine farms and oyster beds.
Cold winter temperatures could help slow the spread of the oil slick by freezing it, officials said.
The barge, which was moving from a construction site off the port of Daesan, lost control after a wire linking it to a tug boat was cut due to high winds, waves and currents, he said.
Kim said the coast guard planned to question the barge's captain to find why he was sailing through the area despite the stormy weather.
The South Korean coast guard says it plans to mobilise dozens of vessels and helicopters in an effort to clean up the slick, said Jung Se-hi, another coast guard official, adding that the operation was expected to take at least three days.
Heavy winds and high waves delayed containment efforts on Friday but seas were calmer on Saturday.
The spill was the country's largest, involving twice as much oil as the worst previous spill in 1995.
The oil slick was a quarter of the size of the 260,000 barrels, or 11 million gallons, of that which was spilled into Alaska's Prince William Sound by the Exxon Valdez in 1989.