Cox admitted in 2010 to using anabolic steroids and accepted a four-year suspension and disqualification of her results from 2001 to 2004.
The International Olympic Committee executive board formally disqualified Cox and took away her gold medal. However, the IOC took no action on the U.S. team victory, which still stands â€" for now.
The Olympic body said it is up to the rules of the International Association of Athletics Federations whether to disqualify the U.S. from the gold.
In a separate case dating back 12 years, the IOC on Saturday reallocated the medals removed from the U.S. men's 4x400 relay team from the Sydney Games because of the admitted doping by the late Antonio Pettigrew.
Cox ran in the preliminaries of the Athens relay. Sanya Richards, Dee Dee Trotter, Monique Henderson and Monique Hennegan ran in the final.
Under current international rules, an entire relay team can be disqualified because of the doping of one member, even an alternate. But IOC spokesman Mark Adams said it wasn't clear whether the IAAF rules were in effect at the time of the Athens Games.
"It is now within the remit of the IAAF to interpret its rules as to whether the disqualification of the athlete would have any effect on the results of the U.S. relay team," the IOC said.
If the U.S. is stripped of the victory, Russia would move from silver to gold and Jamaica from bronze to silver. Britain would get the bronze.
In a previous case, U.S. women's teams were stripped of the gold medal in the 4x400 relay and bronze in the 4x100 relay at the 2000 Sydney Games following admission of doping by Marion Jones.
In the Pettigrew case, the IOC stripped the U.S. team â€" including Michael Johnson â€" of the relay medals in 2008 but had postponed reallocating the medals pending any information from the BALCO doping investigation in the U.S.
Pettigrew died in 2010 from an overdose of sleeping pills.
The IOC decided Saturday to elevate Nigeria to the gold, with Jamaica moving up from bronze to silver and the Bahamas from fourth to bronze.
The IOC said it still waiting for more documents from the U.S. Anti-Doping Agency before acting in the case of Tyler Hamilton, the U.S. cyclist who won the time-trial gold medal in Athens.
After years of denials, Hamilton told CBS's "60 Minutes" last year that he had repeatedly used performance-enhancing drugs. The IOC is considering whether to strip him of the Athens gold and readjust the medals.
IOC President Jacques Rogge said later Saturday that Hamilton's case would be decided in the next two weeks.
Retired Russian rider Viatcheslav Ekimov, who finished second behind Hamilton in Athens, stands to be upgraded from silver to gold. Bobby Julich of the United States finished third in Athens, with Michael Rogers of Australia fourth.
The IOC took no immediate action Saturday on the suspicious results uncovered during recent retesting of samples from the Athens Games eight years ago. IOC medical commission chairman Arne Ljungqvist told the AP this week that he is investigating up to five possible positive results.
The backup "B'' samples haven't yet been tested, and the athletes and sports that produced the adverse results haven't been disclosed. If positive cases are confirmed, the IOC could retroactively disqualify athletes, nullify results and strip medals.
"There is an issue, indeed, with a certain number of athletes (from Athens)," Rogge said, "but the regulations that are in place and are valid ask us to keep the confidentiality until the 'B' sample has been tested. This is not the case yet (so) more, I cannot tell you."
The IOC stores doping samples from each Olympics for eight years to allow for retesting. The statute of limitations for Athens will expire Aug. 29, the date the games closed in 2004.
In 2009, five athletes were caught in retesting of samples from the 2008 Beijing Games for CERA, an advanced version of the blood-boosting drug EPO. Rashid Ramzi of Bahrain was retroactively stripped of his gold medal in the 1,500 meters.
Rogge also said there was no ill feeling on the part of the IOC toward British athletes Dwain Chambers and David Millar, and Olympic hurdles champion LaShawn Merrit, who all were guilty of doping offenses and have returned to compete at the London Games.
Chambers and Millar overturned lifetime Olympic bans through the Court of Arbitration for Sport, which overruled a British Olympic Association rule.
"The athletes have the right to compete, I respect that," Rogge said. "If I meet one of the athletes and he wants to shake my hand, I shake hands with the athlete without any reservations."
