Graham said he would look at the role of former Attorney General Loretta Lynch - who tried to step back from the Clinton email investigation, which led to the broader involvement of former FBI Director James Comey.
"What was the conflict that made Loretta Lynch so unable to preside over the Clinton email investigation?" Graham asked.
While Graham ticked off the boxes of a series of questions which have dominated conservative talk radio over the past two years, the ally of the President made clear he agreed with the Mueller report findings on one very key issue - that the Russians were responsible for the hacking of the Democratic Party in 2016.
“It was the Russians - it wasn’t some 300 pound guy sitting on a bed somewhere,” Graham said, making reference to a quote by President Trump, who at times has rejected assertions that Russian Intelligence was responsible for the hacking of emails from Clinton campaign and DNC officials.
Graham said he also wanted answers on how the Obama Administration handled the initial developments in the Russia investigation - which came during the 2016 campaign.
"Nobody went to President Trump to tell him, there may be some people in your orbit that are connected to the Russians and working with the Russians," Graham said at a news conference.
At the White House, President Trump kept his comments limited about the Mueller report, saying he would not oppose the release of the details of the report, if that’s what Attorney General Barr wants to do.
Asked during an event in the Oval Office whether the Special Counsel had done his job honorably, Mr. Trump responded: "Yes, he did."
“I wish it could have gone a lot sooner, a lot quicker,” the President added.