"The point I'm trying to make is that there's been too many times in the last six months where the President has told people, 'if you don't do what I say, there'll be consequences,' and nothing's happened," Graham told CNN's Dana Bash.
Graham said Putin didn't ignore Obama because of Benghazi alone. He listed Edward Snowden, the ouster of Mohamed Morsi in Egypt, and Obama's threat of a "red line" in Syria as part of a larger "narrative" that paved the way for the conflict between Russia and Ukraine.
"When you tell the world we're gonna find the people who killed our four Americans in Libya, including the ambassador, and you do nothing about it," he said. "Whether you agree with his policy in Syria, Egypt, whether you agree with his policies, when he tells people there will be consequences, and there are none, it sets in motion exactly what you see."
Asked if invoking Benghazi was a just a way for the senator to throw red meat to conservatives back home during primary season, Graham said that voters wanted to know more about the 2012 attack in Libya.
"Everything I've done has been about what I think is best for the country," he said. "I think it's best to find the truth about Benghazi, when my primary's over, and I'm gonna win, I'm gonna still be on Benghazi."