"I'm not going to do any more. Enough already. It's over," Graham said when asked why he would not call for Mueller to testify.
The senator from the US state of South Carolina clarified that he will invite Mueller should there be any dispute about a conversation.
Media outlets reported on Tuesday that Mueller wrote a letter to Barr in late March, accusing the attorney general of not fully capturing the context and work of the special counsel's office in his summary.
The Mueller report concluded that no collusion took place between President Donald Trump's campaign team and Russia but left the decision on whether Trump interfered with the special counsel's probe up to Congress. However, Mueller did say that Moscow attempted to interfere in the US election.
Russia has repeatedly denied interfering in the US political system, saying the allegations against Moscow were made up to excuse Hillary Clinton’s election loss as well as deflect public attention from actual instances of election fraud and corruption.