GOP strategist Karl Rove doubled down Sunday on his doubts about Hillary Clinton's health, which last week drew a sharp rebuke from former President Bill Clinton.

"The Center for Disease Control says a concussion is a type of traumatic brain injury," Rove told his roundtable mates on "Fox News Sunday with Chris Wallace," all of whom took issue, at varying degrees, with the former George W. Bush adviser's comments, reported in a headline by the New York Post's "Page Six," that "Hillary may have brain damage" from a 2012 concussion.

"I'm not questioning her health. What I'm questioning is whether or not it's a done deal that she's running, and she would not be human if she … did not take this into consideration," Rove said while dodging fire for his comments. "She'll be 69 at the time of the 2016 election. If she gets elected and serves two terms, she'll be 77."

After Rove's initial comments last week, former President Bill Clinton defended his wife and lashed out at Rove and conservatives.

"First, they said she faked her concussion and now they say she is auditioning for her part on 'The Walking Dead,'" Bill Clinton said at the Peter G. Peterson Foundation's 2014 Fiscal Summit. "I must be in really tough shape because she is still quicker than I am."

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Clinton later added, "When a question is asked, it has to be answered in a serious fashion if it raises a serious issue, even in a ridiculous way. After that, you just have to trust the people and get back to the business of what's really in the public interest."

Rove said, "I love being lectured by Bill Clinton that this is off-limits: 'You can't talk about her health. You can't talk about her age.' Let's remember this is a guy who ran for reelection by savaging Bob Dole. … [He] looked like Methuselah in the Clinton TV ads."

Despite the Republican strategist's stated confidence in Clinton's health, he said the American people need some proof to confirm her condition.

"Let's be clear: She is going to have to cough up these medical records and describe this, if this was that serious," Rove said.

Chris Wallace was also joined by Dick and Lynn Cheney on Sunday, and the former vice president, who had his own health problems during his tenure in the White House, offered his thoughts on Clinton's concussion.

"I think any presidential candidate or vice presidential candidate is going to have to answer questions about their health," Dick Cheney said. "I wouldn't want to pre-judge Mrs. Clinton's health. I don't know about it.

"I felt responsible to be open about my health when I was vice president and a candidate," he added. "[It's] expected of anyone running."

Echoing Cheney's sentiment, Republican National Committee Chairman Reince Priebus said Sunday that if Clinton did suffer a brain injury, it would bring into question her capability to perform her duties as commander-in-chief.

"I'm not a doctor," Preibus told NBC's "Meet the Press." "What I do know is that the issue is going to come up, as it does for any person running for president."