In a separate interview with ABC's This Week, Clapper said that Russian Federation likely views Comey's firing as "another victory on the scoreboard for them" because "the lead of the investigation about potential collusion between Russian Federation and the Trump campaign has been removed".
Hours later, the White House would neither confirm nor deny the existence of the president's secret recordings.
Ron Nehring, a former committee member and former California Republican Party chairman, said Comey's firing was far more important to journalists and Washington insiders than voters. "You can't be cute about tapes".
Some others who have interacted with Mr. Trump and spent time with him in his office said they didn't witness him record any conversations.
Mr Trump's nominee must be confirmed in the Senate, where Democrats and some Republicans have fiercely criticised Mr Comey's firing. The move prompted an uproar among Democrats and some Republicans because Comey's agency is leading an investigation into whether members of the Trump campaign colluded with Russian Federation in that country's attempts to interfere with the US presidential election previous year. They called the president's tweet a clear attempt at intimidation.
Michael Cohen, Mr. Trump's personal attorney, said, "In the decade that I worked for Mr. Trump, I have never seen a recording device attached to his phone, nor am I aware of any occasion where he taped a conversation".
Trump also took to Twitter to warn Comey that he "better hope that there are no "tapes" of our conversations before he starts leaking to the press".
"The fact that they had a private conversation in which the president, by his own admission, was discussing the future of Director Comey in that job and the president brings up whether he's under investigation?"
Trump's threat about tapes has intensified calls from Democrats for an independent probe of alleged Russian meddling in the 2016 USA election.
Trump addressed the crowd in a five-minute video, telling them their support will help Republicans keep control of the House next year and make gains in the Senate.
Trump said Saturday a new Federal Bureau of Investigation director could possibly be named in the next few days, but whoever it might be is likely to undergo intense questioning at a Senate confirmation hearing, delaying the time when the appointee might actually take over control of the agency. President Donald Trump speaks to members of the media aboard Air Force One before his departure from Andrews Air Force Base, Md., Saturday, May 13, 2017.
"It's in the interest of the American people, it's in the interest of Russian Federation and the rest of the world that we do something to see if we can not improve the relationship between the two greatest nuclear powers in the world", Tillerson said.
Trump fired Comey on Tuesday, at first saying he accepted recommendations from Attorney General Jeff Sessions and his deputy, Rod Rosenstein, that he be ousted because of the role he played past year in the investigation into Trump's presidential election challenger, Democrat Hillary Clinton, and the way she handled national security material on her private email server.
Peter Goldberg, an Alaska committeeman, said Trump's latest tweets about Comey are "just a distraction" and that reaction to the firing is like "a bee buzzing around your head".
Republican leaders in the Senate have rebuffed calls for a special prosecutor, saying it would interfere with ongoing congressional probes.
Graham said that that was exactly what was needed. "We should be friends with our neighbouring countries". At week's end, the president was still fuming over that, and a shake-up of the entire communications team was under consideration by Trump, according to reports by The New York Times and The Wall Street Journal.