The other six contenders, i.e. Sergei Glazyev, Vladimir Malyshkin, Sergei Mironov, Vladimir Putin, Irina Khakamada and Nikolai Kharitonov, remain in the race.
Mr Rybkin cited the predictability of election results as the reason behind his decision. "I do not want to run in front of the presidential motorcade like a hare," said Mr Rybkin.
Mr Rybkin said he had adopted that decision without consulting with Boris Berezovsky, who is financing his campaign. "This was my decision, which does not mean that I betrayed Boris Berezovsky. This will never happen," emphasised Mr Rybkin.
Mr Rybkin is going to take a tour of Russia to set out his political views to Russians.
"I will tour Russia, old Russian towns," Mr Rybkin said without specifying which towns he would visit.
The Central Election Commission (CEC) has not, thus far, received a relative statement from Mr Rybkin, reports the CEC press service.