"Some important people have told me not to put my name on the ballot," Kapkov, who heads the Abramovich-sponsored National Academy Fund which supplies most of the RFU's money, was quoted as saying by local media.
Kapkov, 34, had been one of the favourites to replace Sports Minister Vitaly Mutko, who resigned from his dual role as RFU chief last month after Russian President Dmitry Medvedev demanded that all government officials in charge of national sports bodies should be replaced by professional personnel.
Kapkov's withdrawal leaves former Zenit St Petersburg president Sergei Fursenko, a close friend of Russian Prime Minister Vladimir Putin, as the front runner for the job. The new RFU chief will be elected on February 3.
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