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President Trump and his personal attorney Rudy Giuliani on Monday publicly dared former CIA Director John Brennan to follow through on his threats to sue the administration in the wake of the White House's decision to revoke his security clearance last week.

On Sunday, Brennan denied that he has improperly traded on his access to classified information to trash Trump, telling NBC News' "Meet the Press" that "I don’t believe I’m being political at all."

Brennan added: "If my clearances and my reputation as I’m being pulled through the mud now -- if that’s the price we’re going to pay to prevent Donald Trump from doing this against other people, to me it’s a small price to pay. I’m going to do whatever I can personally to try to prevent these abuses in the future, and if it means going to court, I will do that."

The response from Trump's team on Monday: Bring it on.

"To John Brennan: Today President Trump granted our request (Jay Sekulow and me) to handle your case," Giuliani wrote on Twitter, referring to a fellow Trump attorney. "After threatening if you don’t it would be just like Obama’s red lines. Come on John you’re not a blowhard?"

That was an apparent reference to President Obama's vow in 2012 that any chemical weapons attack by the Syrian government would cross a "red line," which the U.S. government would not tolerate.

A year later, hundreds of Syrians were killed by sarin gas. Afterwards, Obama brokered a multi-nation deal in which Syrian President Bashar al-Assad pledged to remove his chemical-weapons stockpile -- a move that drew President Trump's scorn again this year, in the wake of another chemical attack by the Assad regime.

Also on Monday, Trump himself joined in by taunting Brennan to sue.

"I hope John Brennan, the worst CIA Director in our country’s history, brings a lawsuit," Trump wrote. "It will then be very easy to get all of his records, texts, emails and documents to show not only the poor job he did, but how he was involved with the Mueller Rigged Witch Hunt. He won’t sue!"

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The White House announced last Wednesday that President Trump had revoked Brennan's security clearance, in the first decision to come from a review of access for several top Obama-era intelligence and law enforcement officials.

White House Press Secretary Sarah Sanders read a statement on behalf of the president during the start of a news briefing, saying Brennan "has a history that calls his credibility into question."

Specifically, the president's statement criticized Brennan for falsely telling Congress that the CIA had not infiltrated Senate computers, and for claiming that the unverified Steele dossier was not a factor in 2016 intelligence assessments. In reality, the dossier, written by ex-British spy Christopher Steele and funded by the Hillary Clinton campaign, was a key element of federal authorities' court applications to secretly surveil a top Trump campaign aide.

But former CIA Director Leon Panetta on Sunday claimed Trump may not have had the legal authority to terminate Brennan's clearance unilaterally.

“I think there are questions raised as to whether or not this president has followed the executive order, and whether or not he’s provided due process to those that are going to have their security clearances revoked,” Panetta said, referring to Executive Order 12968. The order establishes procedures for revoking security clearances.

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It was unclear whether any suit by Brennan would target Trump personally, or the administration. Giuliani represents Trump in his personal capacity, and lawsuits against the federal government typically would be handled by Justice Department lawyers or the White House counsel to avoid potential conflicts of interest.

Brennan also has not clarified whether his suit would involve due process violations, as suggested by Panetta, or more general First Amendment issues on the theory that Trump had taken official government action to retaliate against Brennan's speech, or both.

Several former intelligence officials have criticized Trump's move to revoke Brennan's clearance, saying the targeted revocation had the aura of political payback.

However, speaking on CNN's "State of the Union," former Director of National Intelligence James Clapper, one such critic of Trump's decision, acknowledged that Brennan's unfettered comments had become an "issue."

"John and his rhetoric have become an issue in and of itself," Clapper said Sunday. "John is sort of like a freight train, and he's going to say what’s on his mind."

In a follow-up tweet on Monday, Trump questioned the motives of the officials lining up to defend Brennan.

"Everybody wants to keep their Security Clearance, it’s worth great prestige and big dollars, even board seats, and that is why certain people are coming forward to protect Brennan," he wrote. "It certainly isn’t because of the good job he did! He is a political 'hack.'"

Fox News' Travis Fedschun contributed to this report.