Republican National Committee Chairman Reince Priebus on Sunday refused to condemn or defend GOP political operative Karl Rove for his controversial suggestion that Hillary Clinton may have brain damage, but said debate on her health is "fair game."

When asked on NBC's "Meet the Press" if the outspoken former aide to President George W. Bush should apologize for suggesting that Clinton may not have fully recovered from a 2012 concussion, Priebus said the matter was "up to Karl Rove."

But Priebus said that, in general, the health and age of Clinton -- a potential Democratic candidate for president in 2016 -- are "fair game" to discuss.

"It's fair game for Ronald Reagan, it's fair game for [2008 GOP presidential nominee] John McCain," he said. "It's going to be an issue [for Clinton]. … The issue of her health and her age is going to come up."

Priebus refused to speculate on the mental health of Clinton, 66, saying "I'm not a doctor."

But the Wisconsin Republican said he isn't convinced she will run for president, saying that lingering questions regarding her response to the 2012 Benghazi attacks while she was secretary of State, among other issues, may give her pause to seek the presidency.

"Given the month she just had, I actually doubt very much whether she actually will run for president in 2016," Priebus said. "I know a lot of people around her want her to run, and I think that they're purposely creating this environment around her, which is causing us to talk about her today."