Amid questions about whether Russian security was sufficient to head off the threat of militant attacks in Sochi, Mr Obama said the Russians understood the stakes involved in hosting the international event.
Asked what he would tell close friends who wanted to go to the Olympics, Mr Obama said: "I'd tell them I believe Sochi is safe and that there are always some risks in these large international gatherings."
But Mr Obama said he would always feel better if the event were being held in the US "because then we have full control over what happens".
US officials have expressed concerns about the level of co-operation with Russian security officials but Mr Obama said the US has a good sense of the security plan Russia has put in place to protect the athletes and spectators at the games, which start next week.
The President said: "The Russian authorities understand the stakes here. They understand there are potential threats that are out there. And we are co-ordinating with them. We've looked at their plans.
Mr Obama said US officials were not discouraging Americans from attending the Winter Games.
He added: "What I would say is that if you want to go to the Olympics, you should go to the Olympics."