Sen. Lindsey Graham, R-S.C., said Tuesday that the relationship between President Donald Trump and Attorney General Jeff Sessions is "beyond repair" and suggested that a new nominee for the job could be considered after the midterm elections in November.

“The president has lost confidence in Jeff Sessions. And I'm telling you what everybody in the country knows, this is a dysfunctional relationship, we need a better one,” Graham said in an interview on NBC's "Today."

“We need an attorney general that can work with the president, that can lead the Department of Justice. This relationship is beyond repair, I think,” he added.

When asked whether the only problem Trump had with Sessions was his decision to recuse himself from any federal probe into Russian election meddling, Graham replied, “It’s much deeper than that.”

"It's a pretty deep breach," he said.

When asked later by NBC News what he meant by "deep breach," Graham declined to elaborate.

Graham also said that any new nominee must allow special counsel Robert Mueller, who is investigating Russian interference in the 2016 election, “to do his job.”

“Is there somebody who’s highly qualified that has the confidence of the president, will also understand their job is to protect Mueller? Yes, I think we can find that person after the election if that's what the president wants,” Graham said.

That idea, however, was not received well by Senate Majority Leader Mitch McConnell, R-Ky., who later in the day told reporters he had "total confidence" in Sessions and the attorney general should "stay exactly where he is."

Trump has criticized his attorney general both in public and in private since Sessions announced his recusal last year. Earlier this month, Trump called on Sessions to end the Mueller probe, which the president frequently attacks as a "witch hunt."

Relations between the two men seemed to bottom out last week after Sessions, amid a barrage of criticism from Trump, hit back in a rare retort hours after the president said his top law enforcement official "never took control" of the Justice Department.

In an unusual statement, Sessions said, "I took control of the Department of Justice the day I was sworn in, which is why we have had unprecedented success at effectuating the President's agenda."

Graham, meanwhile, told "Today" on Tuesday that Mueller is a "fine man" who is "not on a witch hunt."

“Let him do his job. I've seen no evidence of collusion,” Graham said.

Graham, who ran against Trump in the 2016 GOP primary, was very critical of the businessman-turned-candidate during the race, and in 2017 said Trump would have “holy hell” to pay if he fired Sessions.

But the South Carolina Republican has grown closer to the president over the last 12 months, expressing public support frequently and even going on golf outings with him. And, last week, after the latest round between Trump and Sessions, Graham suggested that Trump deserved a faithful attorney general and might fire Sessions after the November midterm elections.

Graham made similar comments in an interview with Fox News on Monday night.

“I like Jeff but it ain't working,” he said. “If they can’t repair this relationship, and I don’t see that happening, the president deserves an attorney general he feels confident in that can lead the dept of justice in a more effective way.”