Graham, who is currently on a congressional trip in Africa, told McClatchy on Thursday that he was "not interested" in having the former FBI director come speak before his panel.

“He’s done his job,” Graham said about Mueller. "I’m not going to retry the case.”

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Democrats are clamoring for Mueller to testify publicly about his findings on his investigation into Russian election interference and the Trump campaign. Two House panels, the Judiciary and Intelligence committees, have already issued invitations for the special counsel to testify next month.

"The job of the special counsel is to report his findings to the attorney general. I'm neutral on whether he should come and talk about his findings or not. I think his decision not to become a media figure during the investigation itself was both extraordinary and I thought a good decision," Blunt said.

He added that "others" will have to decide "whether he should come and testify or not."

Barr told reporters during a press conference that he had "no objections" to Mueller testifying before Congress.

But Republicans have suggested they are eager to move on from Mueller's two-year investigation, with Trump taking a victory lap shortly after Barr's press conference.

Sen.(R-S.C.), the chairman of the Senate Judiciary Committee, is dismissing calls for special counselto testify about his probe into the 2016 election.“I am also pleased that the Attorney General indicated that he did not have any objection to Mr. Mueller testifying before Congress. If Mr. Mueller were to testify, it could give the Congress and the American people another opportunity to better understand the facts and conclusions that he reached during his investigation," she said in a statement.