Comey's apparent goal in a pre-inauguration encounter with Trump in which the veteran law enforcement official presented details of the dossier was to pressure the soon-to- be-president into letting him keep his job, Trump alleged an interview with the New York Times.
Trump said that about two weeks before his inauguration in January, Comey and other officials briefed him in New York on what US intelligence agencies say was Russian meddling in the election, with the goal of helping Trump defeat Hillary Clinton.
Trump said he thinks Comey told him about the dossier -- which Trump dismissed as "made-up junk" -- to suggest he had something to hold over the president.
"In my opinion, he shared it so that I would think he had it out there," Trump said.
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Asked if he thought Comey was seeking leverage over him, Trump said, "Yeah, I think so."
Trump fired Comey in May and later said he had the FBI's Russia investigation in mind when he did it.
Trump critics point to the dismissal as evidence of obstruction of justice, a potentially impeachable offense.
The Times said the interview with Trump was wide-ranging but dominated by talk of the Russia probe.
Trump has denied any suggestion that he or anyone in his campaign colluded with the Russians.
Trump also told the New York Times that he did not believe he was under investigation by special counsel Robert Mueller, appointed to investigate the Russia affair.
The Times said Trump warned that Mueller would be crossing "a red line" if he looked into Trump family finances not related to the Russia investigation.
"I think that's a violation. Look, this is about Russia," Trump said.
But he did not say what he would do if Mueller did end up looking into non-Russia-related Trump financial dealings.