Their war of words escalated Monday after Comey labeled Trump "morally unfit" for office.
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"If we lose tethering of our leaders to that truth, what are we?" Comey said.
ABC News: Moments that mattered in the Comey interview
Trump tweeted that Comey drafted an exoneration of Hillary Clinton long before he talked to her as part of an investigation into her email practices. He labeled Comey "disgruntled" and accused him and allies of having "committed many crimes." For his part, Comey has said that nine or 10 months into the Clinton probe, he had a "clear picture" where it was going and it's common to draft statements before an investigation is complete.
He offered his version of events, detailing the days right after Trump took office. He said it was shortly after the inauguration when Comey was called into the Oval Office, which is where he says the president asked him to close the investigation into Former National Security Adviser Michael Flynn's ties to Russia.
"First of all, it's unusual for the FBI director and the president to be alone at all," Comey said. "His words were, though, 'I hope you can let it go.' I took the expression of hope as, 'This is what I want you to do.'"
"Was President Trump obstructing justice?" Stephanopoulos asked.
"Possibly," he said. "I mean, it's certainly some evidence of obstruction of justice."
RELATED: Full transcript of the interview from ABC News
The ex-FBI director, who until his firing in May led an investigation into possible ties between Russia and the Trump campaign, acknowledged that it was "stunning" to think that Russia could have damaging information about a U.S. president. But he said that in Trump's case, he could not discount the possibility that the president had been compromised.
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"These are more words I never thought I'd utter about a president of the United States, but it's possible," Comey said.
Comey also said he believed Trump treated women like "pieces of meat."
"A person who sees moral equivalence in Charlottesville, who talks about and treats women like they're pieces of meat, who lies constantly about matters big and small and insists the American people believe it - that person's not fit to be president of the United States, on moral grounds," Comey said.
Trump on Sunday rejected Comey's assertion that Trump had sought his loyalty at a January 2017 dinner, saying "I hardly even knew this guy. Just another of his many lies." He also suggested Comey should be imprisoned, tweeting, "how come he gave up Classified Information (jail), why did he lie to Congress (jail)." There is no indication Comey is under investigation for doing either.
The president began assailing Comey even before the interview came out.
He seized on an excerpt shown Saturday in which Comey said his belief that Clinton would beat Trump in the 2016 presidential election was probably a factor in his decision to disclose the investigation into her emails. Comey, Trump tweeted, "was making decisions based on the fact that he thought she was going to win, and he wanted a job. Slimeball!"
That argument was startling given that Comey's handling of the email investigation, including his disclosure shortly before the election that the FBI had reopened its probe, enraged Democrats. After Clinton's loss, many Democrats blamed Comey, and Clinton herself has said it hurt her election prospects.
Comey again defended his actions, saying he made what he thought was the best decision at the time. Comey said he did not remember "consciously thinking" about the election results as he decided to disclose that the FBI had reopened its investigation into candidate Clinton's email use. But he acknowledged, "I was operating in a world where Hillary Clinton was going to beat Donald Trump, and so I'm sure that it was a factor."
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"I don't remember spelling it out, but it had to have been that she's going to be elected president and if I hide this from the American people, she'll be illegitimate the moment she's elected, the moment this comes out," he said.
Trump fired Comey in May 2017, setting off a scramble at the Justice Department that led to the appointment of Mueller as special counsel overseeing the Russia investigation. Mueller's probe has expanded to include whether Trump obstructed justice by firing Comey. So far, 19 people -- including Flynn and Trump's former campaign chairman, Paul Manafort -- have been charged in the investigation. Flynn and two of the president's campaign aides, Rick Gates and George Papadopoulos, have pleaded guilty and are cooperating with Mueller.
Asked whether he believed Trump ought to be impeached, Comey replied, "I hope not because I think impeaching and removing Donald Trump from office would let the American people off the hook and have something happen indirectly that I believe they're duty bound to do directly. People in this country need to stand up and go to the voting booth and vote their values."
He added: "But you cannot have, as president of the United States, someone who does not reflect the values that I believe Republicans treasure and Democrats treasure and independents treasure. That is the core of this country. That's our foundation. And so impeachment, in a way, would short circuit that."
Trump went on to say Comey will "go down as the worst FBI director in history," and in a tweet early Monday, charged that Comey and others "committed many crimes."
(The Associated Press contributed to this report)
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