Specifically, Romney noted Obama's handling of NSA leaker Edward Snowden and Syrian dictator Bashar al-Assad. Snowden is now residing in Russia under temporary political asylum.
"We are, and I've said this before, geopolitical adversaries," Romney said. "Not enemies but adversaries geopolitically. And Putin lines up with Assad and gave Assad the cover that he needed and won a diplomatic battle with regards to Syria."
Romney characterized Russia's acceptance of Snowden as "a bit of a stick in the eye at America. And I think most observers of the international political scene suggest that Russia has elevated itself in stature and America has been diminished."
The White House shrugged off the comments.
"I obviously disagree with that," press secretary Jay Carney said in response to a reporter at a daily briefing.