"So you don't need a special prosecutor", Graham said on NBC's "Meet the Press" program.
Trump was scheduled to leave Friday for his first overseas trip as president.
In testimony before the Senate Intelligence Committee, acting Federal Bureau of Investigation director Andrew McCabe also pledged that he would inform the panel of any effort by the White House or others to interfere with the agency's probe into alleged Russian meddling in the 2016 election. But critics will question whether Trump is perhaps implying that he recorded his conversations with Comey.
In the news briefing Friday afternoon, White House press secretary Sean Spicer said he had spoken to Mr. Trump and the president had nothing further to add on the tapes tweet.
The FBI probe and parallel congressional investigations have hung over Trump's presidency since he took office in January and threaten to overwhelm his policy priorities.
That admission could expose the president to allegations of interfering with ongoing investigations in possible collusion between his aides and the Russian government during the 2016 election.
That explains why Trump demanded Comey's loyalty.
In terms of the context, the White House's contradictions reflect a degree of internal chaos.
Celtics at Wizards: Watch It!
Here are five things to watch out for when the Boston Celtics and the Washington Wizards meet at 8 p.m. tonight at Verizon Center. In the five home games, Washington has held opponents to 40.9 percent shooting, the second lowest among all playoff teams.
"The FBI is one of our Nation's most cherished and respected institutions and today will mark a new beginning for our crown jewel of law enforcement", President Trump said in a statement.
They can make recommendations, but the president will ultimately make the hiring decision.
In doing so, though, Trump sought to criticize Comey after suddenly firing him earlier this week.
Trump confirmed that asked Comey on three separate occasions whether or not he was under investigation. "He's risky because he may be obstructing justice in terms of the investigation. and secondly his credibility has been destroyed".
Republican Committee Chairman Richard Burr asked McCabe whether he ever heard Comey tell Trump the president was not the subject of investigation.
"As a very active President with lots of things happening, it is not possible for my surrogates to stand at podium with flawless accuracy!"
"I had a dinner with him, he wanted to have dinner because he wanted to stay on", Trump said.
"I think in many ways our institutions are under assault externally, and that's the big news here, is the Russian interference in our election system".