Trump called Ohr a "disgrace" outside the White House and said, "I suspect I will be taking it away very quickly".
Ohr works in the Justice Department's criminal division.
Brennan has repeatedly clashed with Trump on Twitter and on television, calling Trump's failure to denounce Russian interference in US elections at a recent summit with Vladimir Putin "nothing short of treasonous". Ohr knows the co-founder of Fusion GPS-the firm hired by the Clinton campaign to do opposition research on Trump, according to CBS.
A message from Steele to Ohr mentioning "our favorite tycoon" has been interpreted by some as referring to Trump, but may have been about a Russian oligarch whose activities the two had been following.
In a statement released late on Thursday, officials who served under Republican and Democratic officials said they did not necessarily agree with Brennan's harsh criticism of the president but that security authorizations should be based on national security, not politics.
In another development, the former U.S. Navy admiral who led the operation to kill terrorist leader Osama bin Laden is challenging Trump to revoke his security clearance.
Trump has indicated he also was considering revoking security clearances for other critics, including Clapper and Hayden, former national security adviser Susan E. Rice, former Federal Bureau of Investigation director James B. Comey, former Federal Bureau of Investigation officials Andrew McCabe, Lisa Page and Peter Strzok, former deputy attorney general Sally Yates and Ohr.
"I know I've gotten tremendous response from having done that, because security clearances are very important to me", he 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.
Brennan wrote: "Trump clearly has become more desperate to protect himself and those close to him, which is why he made the politically motivated decision to revoke my security clearance in an attempt to scare into silence others who might dare to challenge him".
Trump later said that he stripped Brennan's clearance because of his role in investigating Russia's interference in the 2016 presidential election.
"If anything, I'm giving him a bigger voice", the president said.
According to former acting Central Intelligence Agency director Michael Morell, Gates was out of cell range when the letter was originally released, but he's an "important voice".
"So I think it's something that had to be done", he said. But they noted the power play also could be used to reinforce a case alleging obstruction of justice, following the president's firing of former FBI Director James Comey and his repeated tweets calling for the investigation to end. Trump fired Comey past year.
Trump repeatedly has called the probe a "witch hunt" and sought to discredit those involved in it.