DAVOS, Switzerland:  US Robert Mueller, Director of the Federal Bureau of Investigation (FBI) attends the session "Security is an Always-on World" at the World Economic Forum in Davos 26 January 2006.Tthe World Economic Forum this year is gathering more than 2,300 leaders, officials and executives for five days of high-powered networking.  AFP PHOTO PIERRE VERDY  (Photo credit should read PIERRE VERDY/AFP/Getty Images)

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(CNN) —  

Senate Republicans say it’s time to move on from special counsel Robert Mueller’s investigation.

While House Democrats are ramping up their investigations of President Donald Trump and asking that Mueller testify, Senate Republicans say they don’t see the need to follow up on the Mueller report or bring him before their committees.

“I’m all good, I’m done with the Mueller report,” said Senate Judiciary Chairman Lindsey Graham in an interview with CNN in South Carolina. “We will have (Attorney General William) Barr come in and tell us about what he found. I made sure that Mueller was able to do his job without interference. The Mueller report is over for me. Done.”

Graham and Republican Sen. Joni Ernst, a member of the Senate Judiciary Committee, both told CNN Monday they didn’t think testimony from Mueller would be necessary in the days ahead, a sign of the clear split between Republicans and Democrats about how to pursue the findings from the two-year probe into Trump and his campaign.

PHOTO: Scott Olson/Getty Images

Asked about the Democratic investigations, including the subpoena issued Monday for former White House counsel Don McGahn, Graham said: “Knock yourself out.”

“I thought Mueller would be the final word on this,” he said. “He is for me. If you want to keep doing this, be my guest.”

Graham added: “If you really think he needs to be impeached, have the courage of your conviction just don’t talk about it, do it. “

Ernst, who is up for re-election in 2020, told CNN she expected the GOP-led committee to focus on confirming federal judges rather than the details of the special counsel’s probe, which didn’t charge Trump with a crime but investigated 11 episodes where he sought to undercut the Russia investigation.

While she said there’s a “potential” for hearings, the Iowa Republican added: “But really the House seems all over this, I know that we will continue to work on judges as a primary concern in (Senate) Judiciary.”

“I don’t know that that’s necessary, we have the report so we can go from there,” Ernst said of Mueller testifying, adding that she wanted to focus on efforts to reauthorize the Violence Against Women Act instead.

Ernst’s response showcases the deep divide between Senate Republicans – who are eager to move on – and House Democrats, who want to further probe all elements of the two-year investigation.

Asked if she was alarmed by Trump’s behavior as outlined in the report, Ernst said: “I think we all know who the President is, he has a brash demeanor, that’s about all I can say.”

Graham didn’t mince words when asked about Russia, saying the report made it clear “they are going to try to do it again.”

But Graham also indicated he planned to investigate the dossier compiled by ex-British intelligence agent Christopher Steele.

“The (Steele) dossier was a bunch of garbage,” he said. “I’m going to look into how the dossier was used to get a warrant against an American citizen. Where did it come from? I think the Russians played Steele so the one thing I’ve learned this report and everything else is the Russians are up to no good and we need to push back.”

CNN’s Liz Turrell contributed to this report.