He tweeted that Mr Comey had "better hope there are no 'tapes' of our conversations", suggesting such tapes, if they existed, might contradict him.
Mr Comey, who had been leading an inquiry into possible collusion between Trump election campaign officials and Russia, was fired on Tuesday.
Mr Trump has insisted Mr Comey told him that he was not under investigation.
Once over dinner and twice over the phone, Mr Comey had told him he was not a target of the inquiry, the US president said.
His comments raised accusations among opponents that he was interfering in the investigation.
Mr Trump also said this week that he alone was responsible for the decision to sack Mr Comey, calling him a "showboat" and "grandstander".
But this explanation appeared to undermine earlier comments from administration officials that Mr Comey had been fired on the recommendation of Attorney General Jeff Sessions and his deputy Rod Rosenstein.
The first line of Mr Trump's letter sacking Mr Comey refers to a memo written by Mr Rosenstein and says: "I have accepted their recommendation".
But he later told NBC he was "going to fire him regardless of the recommendation".
A New York Times report said that, during a one-on-one dinner in late January, Mr Trump had asked Mr Comey for a pledge of loyalty but it was not forthcoming.
Apparently angered by criticism of the different accounts of the sacking, Mr Trump used another of his tweets on Friday to say: "As a very active President with lots of things happening, it is not possible for my surrogates to stand at podium with perfect accuracy!"
He added: "Maybe the best thing to do would be to cancel all future 'press briefings' and hand out written responses for the sake of accuracy???"
It was unclear whether Mr Trump's reference to "tapes" suggested there might be secret recordings of conversations that could be used to challenge any statements by Mr Comey, or whether it was simply a way of warding him off from commenting.
But the reference has done nothing to silence the echoes of the Watergate affairthat have resounded around the Russian interference inquiry.
In 1973, President Richard Nixon sacked Archibald Cox, the Watergate special prosecutor who was seeking access to tapes of presidential conversations that ultimately led to Mr Nixon's resignation.
Mr Trump has dismissed the FBI investigation as a "charade" and has said Democrats are using "fake news" about collusion with the Russians as an excuse for losing the election.
In another tweet on Friday, Mr Trump said: "When [former Director of National Intelligence] James Clapper himself, and virtually everyone else with knowledge of the witch hunt, says there is no collusion, when does it end?"
However, Mr Comey's successor, acting FBI Director Andrew McCabe, said on Thursday that it remained "a highly significant investigation".
In testimony to the Senate intelligence committee, he also cast doubt on White House claims that Mr Comey had lost the confidence of his staff.
"I can confidently tell you that the vast majority of employees enjoyed a deep and positive connection to Director Comey," Mr McCabe said.
Separately on Friday, Mr Trump's lawyers said a review of the past 10 years of his tax returns showed "no income of any type from Russian sources". Although there was income from a beauty pageant and the sale of a property, there was "no equity investment by Russians" and no money owed by Russians to Mr Trump, a letter said.