RusAF's anti-doping coordinator said she hoped the athletes' admission could help reinstate Russia, which has been barred from international track and field since November 2015 because of large-scale doping.
Among the trio was sprinter Yulia Chermoshanskaya, a member of Russia's gold-medal winning 4x100m relay team at the 2008 Beijing Olympics.
The relay quartet was last year stripped of gold after Chermoshanskaya tested positive for steroids in a doping retest and was disqualified for two years.
Shot putters Anna Omarova and Soslan Tsirikhov, both disqualified for two years in March, also acknowledged guilt.
"I believe it will not worsen the situation."
Last month Russian hammer thrower Anna Bulgakova, 400m runner Antonina Krivoshapka, shot putter Yevgenia Kolodko, discus thrower Vera Ganeyeva and pole vaulter Dmitry Starodubtsev also admitted to doping.
Russia was banned from international athletics after evidence emerged of state-sponsored doping.
The country was barred from last year's Rio Olympics and will not be able to send a team to this year's World Championships in London in August.
But 12 individual athletes have been allowed to compete as neutrals.
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