Andrew McCabe related the account in an interview aired Sunday on the CBS program "60 Minutes", saying that Trump's comments came despite being told by US intelligence officials that the North did, in fact, possess such missiles.
"This was the illegal and treasonous "insurance policy" in full action!"
McCabe himself was sacked in March 2018 for "lack of candor" in an internal investigation into the FBI's handling of a 2016 probe into Trump's Democratic rival Hillary Clinton. "The president may have been engaged in obstruction of justice in the firing of Jim Comey".
The Republican chairman of a powerful Senate committee has vowed to investigate a claim that Rod Rosenstein, the deputy attorney general, considered trying to remove President Trump from office in 2017.
McCabe also said in the interview that Trump told his top intelligence officials that he believed Russian President Vladimir Putin more than he did FBI investigators.
After Comey was sacked, McCabe said that he ordered two investigations of the President himself.
The plan was crafted in the chaotic days after Comey was sacked, when the FBI began investigating whether President Donald Trump had obstructed justice and whether he might be, wittingly or not, in league with the Russians.
The explosive interview triggered a twitterstorm from President Trump in which he accused McCabe and others Justice Department officials (whom Trump hired) of treasonous activity.
Despite the Russian Federation probe not being mentioned in the memo, Trump still used it as a justification in an interview with NBC News in May 2017, just after the firing of Comey.
Saying he believes the country "needs to know if it happened", Graham said it was simply "stunning" that a leader of the Federal Bureau of Investigation would proudly go on television and brag about the "attempted bureaucratic coup".
The Justice Department's watchdog has referred his findings on McCabe to the US Attorney's office in Washington for possible criminal charges.
Donald Trump lashed out at deputy attorney-general Rod Rosenstein. "I know Rosenstein vehemently denied it, but we're going to get to the bottom of it". I could easily wear a recording device.
"It is saying that we had information that led us to believe that there might be a threat to national security - in this case that the president himself might, in fact, be a threat to the United States' national security", McCabe said. "They wouldn't know it was there, '" recalled McCabe.
Guthrie asked McCabe, "Did you tell the "Gang of Eight" that you had opened a counterintelligence investigation into President Trump?"
The book, the latest in a series of insider accounts about the Trump presidency, is due for release on Tuesday and has surged up the Amazon non-fiction charts on pre-sales.
Alabama woman who joined Islamic State seeks return to US
She told the paper that she wished to return home to Britain , and her family have called for her to be allowed to come home. She gave birth to a baby boy last weekend, after she lost two previous children in Syria and named him after her first son.