Rove said Brennan has been "over-the-top" and "irresponsible" with his criticisms against the president - though he wasn't sure how advantageous it would be for Trump to paint Brennan as the newest member of "the resistance".
"There's no silence", Trump said.
All materials, including briefing reports and memos, audio/video presentations, PowerPoint presentations and any other records, used by CIA Director Brennan and/or other CIA officials to brief Senator Reid and/or members of his staff on alleged "collusion" between the Trump presidential campaign and Russian Federation.
FILE - Former CIA Director John Brennan testifies on Capitol Hill in Washington, May 23, 2017. Clapper and former CIA Director Michael Hayden have appeared on a White House list of people who may also have their security clearances revoked.
Trump defended his move on Brennan on Wednesday, saying it had elevated the former Central Intelligence Agency chief rather than hampered his freedom of speech. It was signed by six former CIA directors, five former CIA deputy directors and a former director of National Intelligence.
In the statement, the officials call the move "unprecedented" and caution against using security clearances as a political tool.
FILE - U.S. Navy Adm. William McRaven addresses the Texas Board of Regents, in Austin, Texas, Aug. 21, 2014.More news: Paul Pogba explains penalty row with Alexis Sanchez
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The retired admiral called Brennan "one of the finest public servants I have ever known".
The president's comments were a swift departure from the official explanation given by the White House earlier Wednesday that cited the "the risks" posed by Brennan's alleged "erratic conduct and behavior".
Brennan has repeatedly clashed with Trump on Twitter and on television, calling Trump's failure to denounce Russian interference in USA elections at a recent summit with Vladimir Putin "nothing short of treasonous".
Trump repeated his belief the probe is a "rigged witch hunt. a sham. and these people led it", referring to Brennan and nine other past and current government security officials whose clearances he is considering revoking.
But Republicans, including some who've been critical of Mr. Trump, said Mr. Brennan has crossed lines with his vicious criticism of the new president.
"Many people don't even know who [McRaven] is, and now he has a bigger voice". "In many cases, I've given him a bigger voice".
"Let him write his report", Trump said. "Mr. Trump's claims of no collusion are, in a word, hogwash", Brennan said.
The extreme action of revoking security clearances is one more instance of Donald Trump undertaking measures that no other president has done, leaving legal analysts in question about whether the action is actually within his authority.