The piece, posted on the New York Times website, came a day after Trump announced he was stripping the security clearance of Brennan, who led the Central Intelligence Agency during most of President Barack Obama's second term and has emerged as one of Trump's fiercest critics.
"There's no silence. If anything, I'm giving them a bigger voice", Trump said.
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 think that Bruce Ohr is a disgrace, with his wife, Nellie", Trump told reporters outside the White House.
In an opinion piece in The New York Times, former CIA Director John Brennan said Trump's decision, announced Wednesday, to deny him access to classified information was a desperate attempt to end Mueller's investigation.
But in an interview with The Wall Street Journal, Trump admitted his decision on Brennan's clearance was linked to the ongoing federal probe into possible collusion between his campaign and Russian Federation to influence the 2016 election.
"I don't want to ever allow a politician or someone in the Oval Office to just so cavalierly toss around security clearances", Brennan said.
Imran Khan to be sworn in as Pakistan's prime minister
Murtaza Abbasi, a PMLN legislator, said in parliament that Mr Khan was "brought here by aliens", a euphemism for the military. Pakistan Tehreek-e-Insaaf, or PTI, has been in the fringes of Pakistan's politics for most of the 20 years of its existence.
I think Bruce Ohr is a disgrace.
Trump challenged the suggestion that he was trying to silence critics by taking away security clearances.
"I didn't mean that he committed treason, but it was a term that I used, 'nothing short of treasonous, '" Brennan said in the interview. Ohr had a role in the investigation into Russia's attacks on the 2016 USA elections, which Trump has called a 'rigged witch hunt, ' and Trump has threatened revoking security clearances for numerous highly-positioned officials involved in that investigation.
In the statement, the officials call the move "unprecedented" and caution against using security clearances as a political tool. "We did nothing. There's no collusion!" the president said. And that's OK with me, because I like taking on voices like that.
Writing in The Washington Post, William H. McRaven said he would "consider it an honour" if Mr Trump would revoke his clearance, as well. Trump said, nevertheless, that Mueller should be allowed to finish a report on Russia's interference in the 2016 US presidential election.
In the op-ed, McRaven, who retired from the Navy in 2014, described Brennan as "a man of unparalleled integrity, whose honesty and character have never been in question, except by those who don't know him".
Russian Federation denies having meddled in the 2016 election, but three US intelligence agencies reported in January 2017 that Moscow had intervened and tried to help Trump beat Democratic presidential candidate Hillary Clinton.
"He's one of the most pivotal witnesses in this whole thing", Elie Honig, a former federal prosecutor for the Southern District of NY, told Blake.