When the Fox News host gushed that Trump's tweet "was a smart way" to make sure Comey "stayed honest in those hearings", the president, pleased with himself, replied, "Well, it wasn't very stupid, I can tell you that".
Trump added: "I mean we're going to have to see in terms - look, there has been no obstruction".
On Thursday, Mr Trump also made it clear that he had not made secret recordings of his conversations with Mr Comey, despite an earlier hint to the contrary.
The tapes saga began in May, just days after Mr Trump fired Mr Comey, who was then leading an investigation into Trump associates' ties to Russian officials.
The New York Times has reported that Mr Trump has considered firing Mr Mueller but has so far been talked out of it by aides.
Trump also reiterated the sentiment he expressed via tweet on Thursday - that he did not make tapes of his and Comey's interactions. When news of Comey's account broke, Trump tweeted that Comey "better hope that there are no "tapes" of our conversations before he starts leaking to the press!".
"While I would certainly hope that the President's most recent statement is true, we will continue to pursue the matter with other witnesses so that the public can be assured that if recordings were ever made, they will be preserved and be made available to the committee and ultimately to the public, as well", he said in a statement.
Comey confirmed those conversations one day before his Senate hearing when he released his opening statement.
As president, Trump could demand that Rosenstein fire Mueller by citing a conflict of interest, but Rosenstein has said he wouldn't follow any order that he didn't think was lawful or appropriate and that he had seen no legitimate basis to dismiss the special counsel. More than a half-dozen aides said they were unaware of any recording devices. The third front is Trump's crimes as president especially obstruction of justice.
Comey told lawmakers in testimony this month that as he laid awake in his northern Virginia bed a week after he was summarily fired, he made a decision to act - in large part because of Trump's tweet.
Relations between the White House and the press continued to deteriorate on Friday as the White House communications team prohibited cameras from filming the White House press briefing.
But among Trump loyalists in the White House and in Congress, there was a spirited effort to validate the claim.
We live in perilous times - times that demand fidelity to first principles. He never produced any evidence. He concluded with a tweet calling the investigation into Russian interference in the election and his campaign's possible involvement a "witch hunt", asking, "when does it end?" On New Year's Eve, he claimed he knew "things that other people don't know" about foreign hacking of last year's election, and that the information would be revealed "on Tuesday or Wednesday". Independents went for Comey over Trump, 47 to 17 percent.
The NBC News/Wall Street Journal poll found 45 percent of respondents said they were more likely to believe Comey's version of events from his June 8 testimony to the US Senate, as opposed to 22 percent who are more likely to believe the commander-in-chief.
Mr Trump, for his part, has publicly admitted that the Russian Federation probe was at least part of the rationale in deciding to fire Mr Comey.