"There's some security things that he did get around that were clearly above his capabilities. The way he departed and how he ended up in Moscow -- now, we still have some questions there," Rogers, who appeared on CBS' "Face the Nation," said.
The Republican congressman said he is concerned about how quickly Snowden arrived in Russia after leaking the National Security Agency information.
"Because of the nature of the information that was stolen, again, nothing to do with Americans' privacy, a lot to do with our operations overseas ... when you look at the totality of the information he took, the vast majority of it had to do with military, tactical and operational events happening around the world," he said.
Rogers also said that he's worried about Olympic athletes' safety in Sochi, where terrorists have threatened to attack.
"The Russians have not been fully cooperative on a security front with sharing information that might be helpful in the securing of, both of our athletes and the participants, people who are there to view the games," he said.