There had been speculation Moscow could boycott the Games entirely after the International Olympic Committee (IOC) on Tuesday 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.
"The final decision of course must be made by the Olympic team," he said.
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.
"I feel for those guys -- I consider many of them friends rather than just acquaintances. I really feel for them," he said of the athletes in the Russian team.
Putin's spokesman Dmitry Peskov earlier Wednesday cautioned against an "emotional" response to the ban.