SEOUL, South Korea >> Three weeks after South Korea’s ferry tragedy, the government on Wednesday said it miscounted the number of survivors, a stunning error and the latest of many missteps that have eroded the nation’s confidence in its leaders.

Coast guard chief Kim Suk-kyoon said only 172 people survived the April 16 sinking of the ferry Sewol — not 174, as the government had been saying since April 18.

Kim said one of the survivors was accidentally listed twice, and he blamed the other mistake on an inaccurate report by a passenger.

Another coast guard officer said the passenger falsely told authorities he had been traveling with someone who had sneaked on board and therefore was not on the ship’s list of passengers. The officer spoke on condition of anonymity because she wasn’t authorized to speak to media on the matter. She said the passenger later told officials he gave wrong information because he had "lost track of things."

Kim also said there are two more missing passengers than authorities previously knew about.

Both are Chinese nationals.

That change raises the number of people feared dead to 304. So far 269 bodies have been recovered, and divers are searching for 35 more people. More than 80 percent of the dead are students from a single high school near Seoul who were on a trip to southern Jeju island.

Families of the victims and many other South Koreans have been highly critical of the government’s handling of the rescue effort, and the regulatory failures that may have allowed the disaster to happen.

Shortly after the sinking, officials announced that 368 people were saved, giving scores of families false hope. There is evidence not only that the ship was overloaded with cargo, but that the agency responsible for ensuring passenger safety has incorrect information about how much the ship could safely carry.

The lengthy, difficult underwater search for bodies off South Korea’s southern coast has deepened the anguish of families of missing people, who have been camping out at a nearby port waiting for the news of their loved ones.

Prime Minister Chung Hong-won told a Cabinet Council meeting that officials must work with "resolve to finish searches" by Saturday to help ease the suffering of relatives of missing people.

Tidal currents, a frequent obstacle for divers, are forecast to be weak until then.

Chung has offered to resign amid public anger over the government’s handling of the sinking.

President Park Geun-hye has accepted his resignation offer but asked him to stay in his post for the time being as the government was dealing with the aftermath of the sinking.

Searches have been hampered by strong currents, bad weather and floating debris inside the ship. A civilian diver fell unconscious while searching and died on Tuesday, the first fatality among divers mobilized since the sinking.

Kim, the coast guard chief, said many victims of the sinking crowded together into two cabins — far more than had been booked into the rooms. Of the 269 bodies retrieved, he said, 235 were wearing life jackets.

All 15 surviving crew members involved in the ferry’s navigation have been arrested, accused of negligence and failing to protect passengers. Improper stowage and overloading of cargo is suspected as a possible reason the ferry sank, and four employees at the ship’s owner who handled cargo on the Sewol have also been arrested.