Korean television news reports said the ferry was sinking and that many of the passengers on board were students on the way to Jeju island, about 100 km (60 miles) off the coast, on school trips.
Those reports could not be confirmed immediately by the coast guard.
The coast guard official, speaking from Mokpo city on the southwest coast, said a rescue operation had been launched but could provide no further details. YTN television said 100 passengers had already been rescued.
The ferry, which also carries cars and trucks, has a capacity of about 900 people.
The reason for the ship's difficulties was not immediately clear. Heavy fog had set in overnight in the area, leading to cancellations of many passenger ferry services to islands.
However, news reports said visibility in the area was fair.
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