The news came a day after the International Olympic Committee (IOC) announced that 23 athletes in total had tested positive in re-tests of 265 samples from the London Olympics.
Russia's track and field athletes have already been suspended since November due to suspicions of a systematic doping programme and the latest positive tests are a further blow to the country's hopes of sending a full team to the Rio Olympics in August.
The ROC said it would not name the athletes until the results of their B-sample tests and following the start of official disciplinary proceedings. That is expected to be next month.
Earlier this week, the ROC said 14 of its athletes from the 2008 Beijing Olympics had tested positive for banned substances.
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The IOC, which stores samples for a decade in order to re-test using newer methods or to look for new drugs, is re-testing samples from past Games in a bid to ban cheats from competing at the Rio de Janeiro Olympics.
Russia is under investigation following a report by the World Anti-Doping Agency (WADA) that suggested a widespread doping programme involving not just track and field athletes.
In a bid to improve its chances of returning to competition in time for Rio, Russia's athletics federation has said it will not include any athletes on its Olympic team who had been banned for doping in the past.
The IAAF, the world governing body of athletics, will decide on June 17 whether Moscow has done enough to clean up its act in order to be readmitted to competition though calls to ban Russian athletes from the Rio Games are growing.
The targeted re-testing of samples from past Games by the IOC has focused mainly on athletes who could potentially compete in Rio and anyone found to have been doping will be banned from those Games.
Several Russian medallists are reportedly among those positive Beijing 2008 Games re-tests, including high jumper Anna Chicherova who won a bronze medal in China and went on to claim gold in London.
(Reporting by Alexander Winning; Writing by Karolos Grohmann, Editing by David Evans, Helen Popper and Clare Fallon)
