"I see no cause when it comes to Mr Mueller", Graham said on CNN.
Republicans strongly cautioned the President and his team to let Mueller do his work.
The president also has always been torn over how to approach the probe.
On Friday, attorneys defending Trump and the company of his personal legal counsel, Michael Cohen, filed to move the lawsuit to federal court and claimed she could owe in excess of $20 million for violating a nondisclosure agreement.
Mr Trump's attacks raised new concerns among members of Congress that he could be seeking to orchestrate Mr Mueller's firing. Lindsey Graham, R-S.C., a Trump ally.
And the White House will Monday face uncomfortable new questions about the Trump team's conduct during the 2016 election after Facebook suspended Cambridge Analytica, a data firm used by President's campaign, over allegations it used the data of 50 million users of the social media site without their permission. Trump has declared that his personal finances were off-limits and a "red line" would be crossed if Mueller chose to delve into the president's business dealings prior to his election. Any dismissal would have to be carried out by Rod Rosenstein, the Trump-appointed deputy attorney general who has publicly expressed support for Mueller.
Trump instead nominated Christopher Wray to lead the bureau. "Free and fair elections are the cornerstone of American democracy and both Republicans and Democrats should be concerned about election integrity".
Senate Democratic Leader Charles Schumer accused Mr Trump of "floating trial balloons about derailing" the investigation.
Other Trump backers have noted that Mueller interviewed with Trump to serve another term as Federal Bureau of Investigation director.
Former FBI official Andrew McCabe memorialized his interactions with President Donald Trump in contemporaneous memos, a person familiar with the case said, and they could become a key piece of evidence in special counsel Robert Mueller's probe. Same with lying James Comey.
"I pledge to the American people, as a Republican, to make sure that Mr. Mueller can continue to do his job without any interference", Graham, who has been at odds with Trump on a number of issues, said.
Mr Trump tweeted: "Wow, watch Comey lie under oath to Senator G when asked 'have you ever been an anonymous source - or known someone else to be an anonymous source.?' He said strongly 'never, no.' He lied as shown clearly on @foxandfriends".
Though the precise contents are unknown, the memos possibly could help substantiate Mr. McCabe's assertion that he was unfairly maligned by the White House. "There is no way for us to know at this point", Schiff said on ABC News' "This Week" on Sunday.
Last month the publisher, Flatiron, moved the release date from May 1 to April 17, citing the public's demand to hear from Comey.
"I hope so", Flake said.
That was followed by unprecedented tweets from the President going after Mueller by name, an approach he's avoided as he's sought to appear accommodating in the investigation.
Just a few Republicans strongly warned Trump against firing Mueller - Senator Lindsey Graham of SC said it could lead to the end of Trump's presidency.