Sanders also said that Trump is reviewing the security clearances of several other former officials, all of whom have been critical of Trump, including former FBI Director James Comey, former Acting Attorney General Sally Yates, former Director of National Intelligence James Clapper, and former Deputy FBI Director Andrew McCabe.
Hayden said Trump's threat would have "no impact on what I think, say or write".
When Mr. Trump addressed Ms. Newman as "that dog" in a tweet, Mr. Brennan replied it is "astounding how often you fail to live up to minimum standards of decency, civility and probity". So far, there's no evidence that anyone acted improperly in conducting the probe, so Trump is resorting to revoking and threatening to revoke security clearance as the only way he can lash out.
A spokesman for Brennan declined to immediately comment.
Mr Brennan's clearance was placed under review last month after he called Mr Trump's meeting with President Putin in Helsinki "nothing short of treasonous".
Bruce Ohr, a Justice Department official.
"I think he is dishonest, he lacks integrity, he has very questionable ethics and morality, and he views the world through a prism of 'how it's going to help Donald Trump?'" Brennan said in an interview with NPR's All Things Considered in April.
Some are claiming this is political retribution, but the overtly political nature of Brennan's attempts to undermine the Trump administration are a real problem.
In a statement from the president read by administration spokeswoman Sarah Huckabee Sanders at the White House, the president accused Brennan of using his access to the nation's secrets for personal benefit.
Mr Trump told the Wall Street Journal that "these people" - including Mr Brennan - had "led" the Russian Federation inquiry.
Clearance to classified information is granted based on a "need to know".
Director of National Intelligence Dan Coats was reportedly not consulted on the revocation.
"If he chooses to do it for political reasons, I think that's a awful precedent, and it's a very sad commentary, and it's an abuse of the system", Clapper said last month when it first emerged that Trump was weighing revoking the clearances of former officials.
Reacting to Sanders' announcement, Reines fired off a series of unhinged tweets, including one in which he labeled President Trump a "vindictive little bitch".
Brennan himself called the action a part of the president's broader effort to "suppress freedom of speech" and "punish critics".
Biden's words were echoed by former ambassador to Russia Michael McFaul, who said that clearance or not, Brennan "will now be just as vigorous & vigilant in defending American values".