There had been speculation Moscow could boycott the Games entirely after the International Olympic Committee (IOC) today barred the country from competition over what its chief Thomas Bach described as Russia's "unprecedented attack on the integrity of the Olympic Games and sport".
Clean Russian athletes would be allowed to compete under an Olympic flag, the IOC said.
"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.
Putin said the ban looked like "an absolutely staged and politically motivated decision", repeating denials that any state sponsored doping programme had existed in Russia.
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Putin's spokesman Dmitry Peskov earlier today cautioned against an "emotional" response to the ban.
Russian officials are expected to address the ban in a meeting next Tuesday.
Politicians and athletes earlier reacted with anger and disappointment to the IOC decision.
Russian media expressed regret at the decision while welcoming the possibility of some athletes participating in South Korea next year, albeit under tight restrictions.
The IOC "chose one of the harshest options it was considering but still not the harshest of all", which would have been a total ban, wrote Kommersant business daily.
"It's very hard to take accusations and punishments. But the fate of our athletes and preserving our place in the Olympic family is more important," wrote the Sport Express daily.
"Can't get by without Russia," the pro-Kremlin Izvestia daily headlined its front page, stressing that "Russian Olympic athletes will defend the honour of the Motherland under any banner."
Some top sports figures agreed, with ice hockey forward Ilya Kovalchuk telling TASS state news agency: "We must go to the Olympics. Refusing is surrender."
Pole vault star Yelena Isinbayeva told TASS: "Addressing our athletes, I want to say that they should absolutely not despair and should continue training for the games."
"This is an absolute outrage," said the last Soviet leader Mikhail Gorbachev, quoted by state RIA Novosti news agency. "This is sport, damn it!" he added.
Nationalist politician Vladimir Zhirinovsky, leader of the Liberal Democratic Party, condemned the decision as "sporting racism, political racism."
Chechen strongman Ramzan Kadyrov, writing on his Telegram social networking page, warned that "not one athlete living in Chechnya will participate under a neutral flag."
Olympic gold-medallist gymnast Svetlana Khorkina, now a ruling party MP, told Sport Express: "What have we come to? Crushing our great country Russia? No, they won't manage it. Russia has an army, nuclear weapons and great people."
Rodchenkov has been living in hiding in the United States since lifting the lid on the intricate workings of a state- supported doping scheme at the 2014 Winter Olympics in Sochi.
"Grigory Rodchenkov is the perfect traitor," wrote tabloid daily Komsomolskaya Pravda.
It said the IOC's actions proved that "you can destroy a whole Olympic country on the basis of indirect evidence and a single witness who was under a criminal investigation and has been treated in a psychiatric hospital".
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