Andrew McCabe also said in the interview with 60 Minutes in the US that the FBI had good reason to open a counterintelligence investigation into whether Mr 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, sacked 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?'" Mr 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 on board with the obstruction and counterintelligence investigations, Mr McCabe replied: "Absolutely."

A Justice Department spokeswoman declined to comment.

Mr McCabe also revealed that when Mr Trump told Mr Rosenstein to put in writing his concerns with Mr 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.

Mr Rosenstein did not want to, Mr McCabe said, and the memo that was made public upon Mr Comey's dismissal did not mention Russia and focused instead on Mr Comey's handling of the Hillary Clinton email server investigation.

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

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

Those actions, including a separate request by Mr 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," Mr McCabe said. "The president may have been engaged in obstruction of justice in the firing of Jim Comey."

Mr McCabe was sacked 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 US Attorney's office in Washington for possible prosecution, but no charges have been brought.

Australian Associated Press