"We need an attorney general that can work with the president, that can lead the Department of Justice," Graham said Tuesday on NBC's "TODAY."
The South Carolina Republican's comments are a significant departure from last summer, when he threatened "holy hell" if Trump fired Sessions and said the firing could amount to the end of his presidency. Last week, however, Graham said that the time to fire Sessions could come "sooner rather than later."
The Justice Department declined to comment.
The rift between Trump and Sessions, which has endured for months, escalated in recent days. On Thursday, the president blasted the former Alabama senator during an interview on Fox News, criticizing Sessions for recusing himself from the Justice Department's investigation of Russian interference in the 2016 election and asking 'What kind of a man is this?'
The president said in the interview that Sessions "never took control of the Justice Department."
Sessions fired back in a statement later that day, saying that he "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."
Trump's critics are concerned that the president could remove the attorney general and appoint a replacement who would stop or limit the Russia probe led by special counsel Robert Mueller. Graham tried to ally those fears during his "TODAY" interview.
He said Sessions, the first senator to endorse the Trump's bid for the presidency, was correct to recuse himself from the investigation.
"Nobody is going to take Jeff's place that doesn't commit to the Senate and the country as a whole that Mueller will be allowed to finish his job without political interference," he said.
The president has repeatedly lashed out at Mueller, accusing him of conducting a "witch hunt" and attacking Sessions for failing to protect him from the probe. Graham alluded to other problems between the two men, however, saying Tuesday that the spat went "deeper" than the Mueller probe.
"It's a pretty deep breach, and here's what I'm suggesting: He's not the only man in the country that can be attorney general," Graham said. "You have to replace him with somebody who is highly qualified and will commit to the Senate to allow Mueller to do his job."
Kevin Bishop, a representative for Graham, declined to elaborate on what deeper issues Graham was referring to. "He said it all right there," Bishop said.
In the interview, Graham said he was sharing "what everybody in the country" already knew: "This is a dysfunctional relationship. We need a better one."
— CNBC's Kevin Breuninger contributed to this report.