"Thirty days in the hospital? And when she reappears, she's wearing glasses that are only for people who have traumatic brain injury? We need to know what's up with that," the report quoted him saying, adding that he "repeated the claim a number of times to the audience."
Rove distanced himself from the Page Six story Monday, telling the Washington Post "of course she doesn't have brain damage."
Still, he said it was clear that Clinton suffered "a serious health episode," and she would "have to be forthcoming" with details of the injury if she ran.
Clinton's diagnosis was a blood clot behind her right ear, between her brain and her skull, that formed when the flu-weakened secretary fell in her Washington, D.C., home in December 2012. She went to a hospital for tests, then was later admitted for three days (not 30) to New York-Presbyterian Hospital.
At the time, some Republicans accused Clinton of faking a case of the "Benghazi flu" to avoid testifying, an assertion Rove says he does not subscribe to.
"She didn't feign illness," he said.
It's too soon to know if the House committee investigating the Benghazi attacks will succeed in uncovering the evidence of a cover-up Republicans have been hunting for over past 20 months, or if any of its findings will stick to then-Secretary of State Hillary Clinton and damage a potential 2016 presidential run.
Rove's comments indicate he hopes to encourage a different tack of undercutting Clinton's presidential qualifications -- her age and health. Clinton will be 68 years old in January 2017, when President Obama's successor takes the oath of office.
"She would not be human if it didn't enter into her considerations," he said Monday.
Democrats pushed back hard on Rove's hints at any frailty in Clinton's health, issuing a blistering statement from the Democratic National Committee.
"It appears Karl Rove's medical diagnoses are about as solid as his election night prognostications," the statement said.
"Please assure Dr. Rove she's 100 percent," a representative for Clinton assured.
"Karl Rove has deceived the country for years, but there are no words for this level of lying," Clinton spokesman Nick Merrill said. "She is 100 percent. Period."
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