WASHINGTON -- Former FBI Deputy Director Andrew McCabe said in an interview that aired Sunday that a "crime may have been committed" when President Donald Trump fired the head of the FBI and tried to publicly undermine an investigation into his campaign's ties to Russia.

McCabe also said in the interview with "60 Minutes" that the FBI had good reason to open a counterintelligence investigation into whether Trump was in league with Russia, and therefore a possible national security threat, following the May 2017 firing of then-FBI Director James Comey.

"And the idea is, if the president committed obstruction of justice, fired the director of the of the FBI to negatively impact or to shut down our investigation of Russia's malign activity and possibly in support of his campaign, as a counterintelligence investigator you have to ask yourself, "Why would a president of the United States do that?" McCabe said.

He added: "So all those same sorts of facts cause us to wonder is there an inappropriate relationship, a connection between this president and our most fearsome enemy, the government of Russia?"

Asked whether Deputy Attorney General Rod Rosenstein was onboard with the obstruction and counterintelligence investigations, McCabe replied, "Absolutely."

A Justice Department spokeswoman declined to comment Sunday night.

McCabe also revealed that when Trump told Rosenstein to put in writing his concerns with Comey -- a document the White House initially held up as justification for his firing -- the president explicitly asked the Justice Department official to reference Russia in the memo. Rosenstein did not want to, McCabe said, and the memo that was made public upon Comey's dismissal did not mention Russia and focused instead on Comey's handling of the Hillary Clinton email server investigation.

"He explained to the president that he did not need Russia in his memo," McCabe said. "And the president responded, "I understand that, I am asking you to put Russia in the memo anyway."

Trump said in a TV interview days after Comey's firing that he was thinking of "this Russia thing" when he fired Comey.

Those actions, including a separate request by Trump that the FBI end an investigation into his first national adviser, Michael Flynn, made the FBI concerned that the president was illegally trying to obstruct the Russia probe.

"Put together, these circumstances were articulable facts that indicated that a crime may have been committed," McCabe said. "The president may have been engaged in obstruction of justice in the firing of Jim Comey."

McCabe was fired from the Justice Department last year after being accused of misleading investigators during an internal probe into a news media disclosure. The allegation was referred to the U.S. Attorney's office in Washington for possible prosecution, but no charges have been brought. McCabe has denied having intentionally lied and said Sunday that he believes his firing was politically motivated.

"I believe I was fired because I opened a case against the president of the United States," he said.

In the interview Sunday, McCabe also said Rosenstein in the days after Comey's firing had proposed wearing a wire to secretly record the president. McCabe said he took the remark seriously, though the Justice Department last September -- responding last September to a New York Times report that first revealed the conversation -- issued a statement from an unnamed official who was in the room and interpreted the remark as sarcastic.

McCabe said the remark was made during a conversation about why Trump had fired Comey.

"And in the context of that conversation, the deputy attorney general offered to wear a wire into the White House. He said, "'I never get searched when I go into the White House. I could easily wear a recording device. They wouldn't know it was there,'" McCabe said.

In excerpts released last week by CBS News, McCabe also described a conversation in which Rosenstein had broached the idea of invoking the Constitution's 25th Amendment to remove Trump from office. The Justice Department said in a statement that Rosenstein, based on his dealings with Trump, does not see cause to seek the removal of the president.

Sen. Elizabeth Warren, a Massachusetts Democrat who is seeking her party's nomination for president, told reporters after a campaign event Sunday in Las Vegas that if the people around Trump believe he cannot fulfil the obligations of his office, then they have a duty to invoke the 25th Amendment.

A favourite target of Trump's ire, Warren said she has no special knowledge on whether there are grounds to remove Trump from office but said that "there are a whole lot of people who do see him every day who evidently were talking about invoking the 25th Amendment."

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Associated Press writer Michelle Price in Las Vegas contributed to this report.