Paul Hamm, who became the first American to win the Olympics men's all-round gymnastics title, should not have been awarded the gold, the sport's governing body ruled on Saturday.
But Hamm would keep his medal despite a scoring error which robbed South Korean bronze medallist Yang Tae-young of the title, the FIG said.
"The FIG rules do not allow for a protest against judges' marks. The judges' marks have to be accepted as a final decision and cannot be changed."
The South Koreans, though, say they will now take their case for Yang to be awarded the gold to the Court of Arbitration for Sport.
Three technical judges, one of them an American, were suspended on Saturday after South Korea's protest over the difficulty level score of Yang was upheld.
Had Yang been credited with the correct difficulty score on the parallel bars, he would have finished with a total of 57.874, 0.051 of a point ahead of his American rival.
"We want fairness and justice in judging practice. Athletes are trying their best to follow the rules and judges should do their best to follow their rules," said South Korean spokeswoman Yoo Jae-soon.
"It has nothing to do about one of the judges being an American. That was just a coincidence. We want justice. We are going to take this to the Court of Arbitration for Sport."
At the 2002 Salt Lake City Winter Games, South Korea speed skater Kim Dong-sung lost the men's short track gold after a questionable call.
The gold went to a U.S. skater, Apolo Ono, sparking weeks of anti-U.S. protests in South Korea.
The FIG re-examined the men's all-round competition on Friday after the South Korean delegation said Yang's routine had not been correctly assessed by the officials during Wednesday's competition.
"The judges' error is confirmed by the FIG, the gymnast was given a start value of 9.9 instead of a 10," the governing body said in a statement.
"In order to protect the integrity of the FIG, the judges, and to be able to maintain and ensure the highest possible judging standard at the Olympic Games, the FIG executive committee has decided to suspend the three technical officials concerned pending inquiry."
The FIG's initial refusal to reveal which score the South Korean's were protesting against had raised some confusion but it emerged on Saturday that it was the start value of Yang's parallel bars routine that had been under scrutiny.
