"We supported athletes who made a decision to compete under a neutral flag before and we are doing the same now".
Any Russian athlete who does compete in Pyeongchang must do so as an "Olympic Athlete from Russia" (OAR), in uniforms bearing that acronym.
Answering a question about uncertainty surrounding the participation of USA athletes in the global sports event held on the Korean Peninsula, she said Washington would continue monitoring the situation in the region in order to ensure protection of its athletes.
Mr. Putin rejected the claims and said the ban was "politically motivated". "We will not prevent our Olympic athletes from taking part if anyone wants to take part in a personal capacity".
It's acceptable for Russian athletes to compete under the IOC's terms, two-time gold medalist pole vaulter Yelena Isinbayeva said, according to Interfax.
Putin, who often uses Russia's Olympic tradition as an example of the country's greatness and showers medalists with luxury cars and cash, had earlier said that competing under a flag other than Russia's would be "humiliating".
He also argued that the International Olympic Committee decision on Tuesday to ban the Russian Federation team from the Winter Games in South Korea for anti-doping violations at the 2014 Sochi Games had political underlining.
Medvedev was referring to a March presidential election in which incumbent Vladimir Putin is standing for re-election.
There were concerns that the Russian president, who has long refuted allegations of systematic doping and criticised the investigations, may announce a complete boycott of the Games as a result.
"So there are still more questions than answers and they all need to clarified".
The Winter Games are to be held February 9-25 in Pyeongchang, a city about 50 miles from the demilitarized zone that separates North and South Korea.
Putin's spokesman, Dmitry Peskov, told reporters it's too soon to discuss the fate of Deputy Prime Minister Vitaly Mutko, who was banned by the International Olympic Committee from all future Olympics after being implicated in the doping scandal as sports minister during the Sochi Games.