Bach stated that he had "taken note" of Putin's announcement, the International Olympic Committee president adding: "I hope and I'm confident that the clean Russian athletes will seize this opportunity to participate at the 2018 Winter Games to represent a new generation of clean athletes".
The IOC ruled Tuesday individual Russians may still compete as an "Olympic Athlete from Russia". That is, if Russian President Vladimir Putin allows them to go to the February 9-25 games.
"Every time they were tested there has not been a single positive result, so we are clean".
"I don't want to evaluate the decision of the International Olympic Committee in relation to me personally. I really feel for them", he said of the athletes in the Russian team.
The International Olympic Committee made a decision to ban the Russian federation as punishment for widespread doping Olympic officials believe was supported by the government.
"They have been preparing for these competitions for their whole careers, and for them it's very important".
He said including the word "Russia" in the team name was a key issue.
Having consistently denied the allegations of a state-backed doping campaign, Russian Federation was banned from PyeongChang 2018 on Tuesday over the country's "systemic manipulation" of the rules, following a 17-month investigation carried out by the former president of Switzerland, Samuel Schmid.
But Sorokin insisted that decision had no impact on the World Cup.
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Putin also said Russian Federation still did not accept accusations that it ran a state-backed doping system around the Sochi Olympics.
Russian athletes will be free to take part in the 2018 Pyeongchang Winter Games under the Olympic flag, Russian President Vladimir Putin said.
Russian media expressed regret at the decision while welcoming the possibility of some athletes participating in South Korea next year, albeit under tight restrictions. Mr Mutko has been accused of presiding over a systematic cover-up of doping in Russian sport.
The IOC Executive Board on Tuesday had said that the ROC was to reimburse the costs incurred by the IOC on the investigations of doping and to contribute to the establishment of the Independent Testing Authority (ITA) for the total sum of $15 million.
The sanctions could be challenged at the Court of Arbitration for Sport.
"We will certainly not declare any boycott, we will not prevent our Olympians from competing, if they want to take part in a personal capacity", Putin said after a speech at an automobile plant in Nizhny Novgorod, in which he announced he would run for a fourth presidential term next year.
The bans came as the result of an International Olympic Committee investigation into allegations of state-backed doping among Russian competitors and sample tampering by laboratory and security officials at Sochi.
The CEO of the Sochi Olympics, Dmitry Chernyshenko, also had his place on an Olympic panel overseeing the 2022 Beijing Winter Games withdrawn by the IOC. The IOC report, chaired by Samuel Schmid, the former president of Switzerland, concluded that there was systematic, state-supported cheating in Russian Federation.