On Twitter, Trump appeared to suggest that if Comey gave his version of contacts between them, the administration might produce tapes of conversations, although it was not clear if such tapes exist.
Two White House officials said some of Trump's frustration centres on what he views as unfair coverage of his decisions and overly harsh criticism of press secretary Sean Spicer, as well as deputy press secretary Sarah Sanders, who led much of the response to Comey's firing.
Trump also hit back on Friday at media reports questioning the credibility of White House accounts of why Comey was sacked, which have changed over the course of the week, and threatened an end to regular White House press briefings.
Republican Senator Lindsey Graham told NBC on Sunday that Trump should turn over any tapes he has of his conversations with the former Federal Bureau of Investigation chief. Nearly all of them [the candidates] are very well known.
Writing unsubstantial, provocative tweets while simultaneously overseeing the significant process of choosing a director for the F.B.I., there is a growing move to hold Trump to account.
Trump has said a decision could come before he leaves Friday for the Mideast and Europe, his first overseas trip as president.
A White House official has said Trump is considering 11 people to replace Comey. Suffice it to say Comey's decision not to alert the public about that investigation wasn't among the list of grievances included in the Justice Department memo Trump cited as justifying his termination. Later, Trump again shifted his rhetoric, saying that he had already made a decision to fire Comey before he got Rosenstein's memo.
"That's, frankly, offensive", Spicer said.
Four candidates to be the bureau's director were in line Saturday for the first interviews with Attorney General Jeff Sessions and his deputy, Rod Rosenstein, at Justice Department headquarters.
Huckabee Sanders isn't the only White House official who has posted tweets about FBI investigations that are very awkward in hindsight.
Republican Senator Lindsey Graham of SC said on Sunday there may come a time when a special prosecutor is needed but not now.
Comey has not publicly discussed any conversations he has had with Trump. Trump said he would make up his mind whether to scrap the briefings "over the next couple weeks".
"Regardless of recommendation I was going to fire Comey.Knowing, there was no good time to do it".
After the election, he began investigating Trump's alleged ties to Russia as well as a series of cyber attacks against Clinton's campaign, which Democrats claimed were conducted by Russian hackers and aimed at influencing the outcome of the vote.
Speaking to CNN on Sunday, Clapper said that the "very disturbing" dismissal last week highlighted clashes between the intelligence community and the Republican president, who has been accused of getting help from Russian Federation to win the race for the White House. Moscow has denied any such meddling.
According to the AP report, sources within the Trump administration that enjoy personal contact with the president assert that he "increasingly sees himself as the White House's only effective spokesperson".