One of the world's major winter sports powers, Russia was on Tuesday banned from taking part in February's Winter Olympics after the IOC found the country had engaged in "systemic manipulation" of anti-doping rules.
However, Russian athletes who can prove that they are clean will be "invited" to compete under the name "Olympic Athlete from Russia" (OAR).
"We, without doubt, will not declare a blockade, we will not prevent our Olympians from taking part [in the Games], if one of them wants to take part in a personal capacity," said Putin on Wednesday, according to the state run RIA news agency.
It had been unclear whether the Kremlin would allow Russian athletes to compete in South Korea as Putin had said in the past that it would be a humiliation to compete without any national symbols.
Speaking at the Gorky Automobile Plant, where he announced he will run for re-election next year, Putin drew attention to the fact that many athletes, including those he knew personally, had been preparing for the Winter Olympics throughout their careers.
"This is very important for them," he added. "Based on these considerations, of course, we will not forbid anything to anyone, block anything, making any impossible conditions for participation."
The Russian President called the ban a politically motivated decision, saying: "It all looks like an absolutely staged and politically motivated decision. We see this, for me there is no doubt about it."
He also questioned how the Games would be organized and said it was not yet fully understood on the Russian side how the team competitions would be organized.
"Under what symbols will they go? This is also not an idle question," he said.
"But in the end, the athletes will have to make a decision themselves, each of them for themselves, both in the team and individually: who and how will participate."
Will Russian stars compete?
Looking ahead to the process of determining which Russian athletes were "clean," WADA President, Sir Craig Reedie, said on Tuesday that it must be proven that the athletes had not been "implicated in the institutionalized scheme and have been tested as overseen by the panel."
Prior to Putin's statement, some prominent Russian Olympians had said they had not yet decided if they would compete.
Evgenia Medvedeva, a two-time world figure-skating champion, told reporters after the IOC's decision that it was "too early" for her to decide whether she would take part.
Figure skating is one of the most popular Winter Olympics events, and the loss of Medvedeva -- widely tipped for a gold medal -- would be a major blow to fans.
Former pole vault world champion Yelena Isinbayeva, one of the most high-profile sports people in the country, had urged on social media for her compatriots not to boycott the Games.
Isinbayeva, who was not allowed to compete at last year's Summer Olympics in Rio because of the ban athletics' governing body the IAAF imposed on Russian athletes, posted on Instagram: "I will call on all the athletes from our country not to even speak the word 'boycott' out loud, because they should understand they have a chance. I didn't have a chance last year."
'Defending the interests of our athletes'
Earlier on Wednesday the Russian government had said it would "seriously analyze" the decision to ban the country from the forthcoming Games before deciding on its response to the ruling.
One leading Russian politician had described the IOC's decision as humiliating, but in his regular call with journalists, Kremlin spokesman Dmitry Peskov said that many questions remained unanswered and that it would be "incorrect" to give into any emotions.
He went on to say that the outstanding questions need to be tackled before any "consolidated position comes from the Olympic assembly" or Russian athletes.
Answering a question on possible action against Russian officials, Peskov said he was not able to comment but added: "This is not a priority, our priority is defending the interests of our athletes, Russian athletes, and we must concentrate all of our efforts on that first, then deal with everything else later."
The reaction to the IOC's ban has been mixed in Russia.
Chairman of the Russian Parliament Igor Lebedev said the decision was 'humiliating and insulting to great sporting Russia', while head of Russia's Olympic Committee Alexander Zhukov said "one of the positive decisions is that all doping-related sanctions and investigations against Russian athletes will be stopped from this moment."
Foreign Ministry spokeswoman Maria Zakharova said on her Facebook page that the country would "survive."
"They are constantly trying prove the absurdity of everything to us: our way of life, culture, history and now sport," she wrote. "Is it painful? Very. Heart and soul are now with our athletes. Will we survive? Yes.
"What have we not had to historically endure from our 'partners.' Well, we cannot be overwhelmed. Neither by world war, nor the collapse of the Soviet Union, nor sanctions ... We will take them all and survive."
'Sad commentary on sport'
Richard McLaren, whose reports into Russian doping -- the second of which was published last year -- provided much of the basis for the IOC's decision, told CNN that the scandal was a "sad commentary on sport," but added that he was pleased his work had been confirmed by the IOC's decision.
A 17-month IOC investigation, carried out by the former president of Switzerland, Samuel Schmid, was tasked with looking at whether or not the Russian government and authorities had played a part in covering up doping of the country's athletes during the 2014 Sochi Winter Olympics.
Schmid's report confirmed "the systemic manipulation of the anti-doping rules and system in Russia."
Separately, the parallel Oswald Commission -- headed by another Swiss, the IOC member, Denis Oswald -- is dealing with the specific cases and determining sanctions against individual athletes.
Twenty-two Russian athletes who were disqualified from the Games and have had results and medals stripped for doping offenses related to the Sochi Winter Olympics in 2014, have filed an appeal against the IOC Disciplinary Committee's rulings with the Court of Arbitration for Sport (CAS) in Lausanne, according to a CAS statement.
The athletes had been retrospectively sanctioned by the IOC following work carried out by the Oswald commission.