Regarding firing Sessions, Graham said, "They'd do it before, but they're anxious about the effect it would have on the midterms themselves".
"Our Justice Department and our Federal Bureau of Investigation - at the top of each, because inside they have incredible people - but our Justice Department and our Federal Bureau of Investigation have to start doing their job and doing it right and doing it now", Trump said.
"What's happening is a disgrace, and at some point ... if it doesn't straighten out properly ..."
At a rally in IN on Thursday night, Trump turned up the rhetoric, threatening to "get involved" in the work of the Justice Department and Federal Bureau of Investigation unless the agencies "start doing their job".
But despite Trump's unhappiness with Sessions, when asked if he would keep him employed past midterms, Bloomberg reports, Trump declined to answer. Several aides said Graham is annoyed with Sessions because he opposes a criminal justice reform bill he supports.
Meanwhile, Trump's lawyers had previously warned a dismissal of Sessions would help special counsel Robert Mueller in his investigation of any potential obstruction of justice involving Trump.
In the interview, Trump gave a token indication Sessions' fate wasn't sealed. "I view it as an illegal investigation". The recusal allowed Deputy Attorney General Rod Rosenstein to appoint Mueller to investigate Russian Federation in May 2017, just days after the president fired FBI Director James Comey. He charged that Mr Mueller's probe was "highly conflicted" and that "real corruption goes untouched". It quoted one Republican Senate aide as saying Trump is venting his dissatisfaction with Sessions to "any senator who will listen".
The president - who did not address the specifics of the charges, just the political impact - has previously pressed Mr Sessions to investigate his perceived enemies and has accused him of failing to take control of the Justice Department.