The director general of the World Anti-Doping Agency, Olivier Niggli, said: "Wada is very mindful that this criminal attack, which to date has recklessly exposed personal data of 29 athletes, will be very distressing for the athletes that have been targeted and cause apprehension for all athletes that were involved in the Rio 2016 Olympic Games.
"To those athletes that have been impacted, we regret that criminals have attempted to smear your reputations in this way and assure you that we are receiving intelligence and advice from the highest level law enforcement and IT security agencies that we are putting into action.
"Given this intelligence and advice, Wada has no doubt that these ongoing attacks are being carried out in retaliation against the Agency, and the global anti-doping system, because of our independent [Dick] Pound and [Richard] McLaren investigations that exposed state-sponsored doping in Russia.
"We condemn this criminal activity and have asked the Russian government to do everything in their power to make it stop.
"Continued cyber-attacks emanating from Russia seriously undermine the work that is being carried out to rebuild a compliant anti-doping program in Russia."
Indeed, Russia faces an extension of its exile from world sport over the hacking of the drug-testing records of every athlete at the Rio Olympics. The nation was warned on Wednesday the leak of secret data by Fancy Bears had harmed its hopes of being reintegrated into the sporting community following bans imposed on it from Rio.
Russia reacted with typical defiance to the claims that the hack had been orchestrated from within its borders. But the president of Wada, Britain's Sir Craig Reedie, was in no doubt about it origin.
Russia has been declared non-compliant with the Wada Code since it was found guilty of state-sponsored doping. Regaining compliance is seen as crucial step in its rehabilitation, and could sway the decision of the International Association of Athletics Federations and International Paralympic Committee to lift the bans imposed on it for its transgressions.
Reedie told Telegraph Sport: "I have been told that we have authoritative information on the identity of these people. At the moment, we're working on trying to make Rusada compliant, and this doesn't make it any easier."
Russia's sports minister, Vitaly Mutko, earlier denied there had been any government involvement in the hack. "How? how?" he said when asked whether there were state links to the Fancy Bears group.