Without identifying Rodchenkov by name, Putin said the IOC's decision had been "mainly based on the testimonies of a person whose moral and ethical attitudes and psychological state raise many questions".
When asked if a final decision on participation had yet been made, Haley added: "There's an open question".
"To participate in the Olympics is an athlete's right. I have not heard anything about that, but I do know in the talks that we have - whether it's Jerusalem or North Korea - it's about, how do we protect the USA citizens in the area?"
Then, on Monday, the United States began military drills with South Korea that were to include simulated strikes on the North's nuclear and missile sites, leading Pyongyang to accuse Washington of pushing the peninsula "to the brink of nuclear war".
The most recent ballistic missile test was conducted by Pyongyang in late November.
Alfons Hörmann, President of the German Olympic Sports Confederation, also claimed he would understand if his country's athletes did not want to compete because of safety concerns.
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On December 5, the IOC chose to suspend membership of the Russian Olympic Committee, which bars the Russian national team from competing at the PyeongChang 2018 Olympics under the national flag.
Putin, who announced on Wednesday he would run in a Russian presidential election next year, said he had not instructed officials to deliver victory for the Russian team at the Sochi Games.
The International Olympic Committee (IOC) ruled Tuesday that individual Russian athletes could still participate in the 2018 Games if they prove to a panel that they have been clean. Russian Deputy Prime Minister Vitaly Mutko today said his life ban from the Olympic Games was "secondary" to those faced by the country's athletes in the wake of this week's IOC ruling.
"With the Olympic Truce resolution, the UN General Assembly is creating the conditions for all athletes to compete in peace".
"They make it possible for all the Olympic athletes to realise their dream of a lifetime".