Russia, a track and field powerhouse, was suspended by the IAAF in November following a WADA panel report that found state-sponsored cheating.
"Serious mistakes have been made by the federation management, along with athletes and coaches who have broken anti-doping rules and neglected the principle of fair play," said Vitaly Mutko, writing in British newspaper The Sunday Times. "Let us be clear. We are ashamed of them."
"We are very sorry that athletes who tried to deceive us, and the world, were not caught sooner. We are very sorry because Russia is committed to upholding the highest standards in sport and is opposed to anything that threatens the Olympic values."
Russia will discover on June 17 whether its athletics federation has met the reform criteria to return to competition in time for the Rio de Janeiro Olympics.
"We do not deny having a problem in Russia, and we are doing everything possible at state level to eradicate doping, including punishing athletes and coaches," Mutko wrote.
"We have done everything that has been asked of us by the IAAF in order to be reinstated," Mutko added. "It would be unjust to demand all these changes and measures, witness them happen, and then still punish Russia's athletes."
