She added Brennan's "lying and recent conduct, characterized by increasingly frenzied commentary, is wholly inconsistent with access to the nation's most closely held secrets".
In an interview on CNN's "New Day" Thursday, Clapper called Trump's drawn connection from the Russian Federation investigation to revoking Brennan's clearance a "candid admission" and "very disturbing".
"And these people led it", Trump said, referring to Brennan and nine other past and current government security officials whose clearances he is considering revoking. "A good leader always puts the welfare of others before himself or herself", but "through your actions, you have embarrassed us in the eyes of our children, humiliated us on the world stage and, worst of all, divided us as a nation", he wrote.
"I don't trust many of those people on that list", Trump said Wednesday.
And Brennan might not be the only former intelligence or national security official to have his clearance taken away; the president has threatened others as well.
"There needs to be an official determination made about this, and that, I think, can only be done by the Mueller investigation", Clapper told CNN on Thursday.More news: Primaries in Connecticut, Vermont, Minnesota and Wisconsin
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Former high-ranking officials typically retain their security clearance when they leave office so their successors can consult with them on sensitive issues. After Trump's attack this week on former White House aide Omarosa Manigault Newman, Brennan tweeted that the president failed "to live up to minimum standards of decency, civility, and probity".
Writing in an article for the New York Times published on Thursday, Brennan hit back after being stripped of his security clearance by the White House the previous day citing "erratic conduct and behavior".
On his Twitter account, Trump reposted several comments supporting his revocation of Brennan's clearance, including one from Sean Hannity, a conservative Fox News television host. "I don't know why they give them security clearances anyway other than maybe a transition period", Shelby added.
Following the president's summit last month with Russia's Vladimir Putin, Brennan - who headed the Central Intelligence Agency under Obama - described Trump's behavior as "nothing short of treasonous".
"I think it is pretty clear this is a president who goes out of his way to punish his political adversaries".
White House spokeswoman Sarah Huckabee Sanders announced the decision at a White House briefing Wednesday. U.S. Representative Joaquin Castro said Mueller should also investigate the issue now that Trump tied it to the Russian Federation probe.