Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellObama calls on Senate not to fill Ginsburg's vacancy until after election Planned Parenthood: 'The fate of our rights' depends on Ginsburg replacement Progressive group to spend M in ad campaign on Supreme Court vacancy MORE (R-Ky.) said Saturday he doesn’t think Congress has any role in protecting special counsel Robert Mueller from potentially being fired by President Trump.

“I don’t hear much pressure to pass anything,” McConnell said in an interview with Hugh Hewitt. “There’s been no indication the president or the White House are not cooperating with the special counsel.”

“I think the view up here is, let him do his job,” McConnell continued.

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McConnell’s comments come after the first indictments were handed down in Mueller’s investigation into Russian election interference last week.

Trump’s former campaign chairman Paul Manafort was charged on multiple counts, including conspiracy against the United States and money laundering related to his work for a pro-Russia political party in Ukraine. His former business associate, Richard Gates, was also indicted.

It was also announced Monday that former Trump campaign adviser George Papadopoulos pleaded guilty earlier this month to lying to FBI agents about his contacts with Russian officials.

Senators have previously offered two bills that would protect Mueller from being fired by Trump.

One proposed bill, from Sens. Lindsey Graham Lindsey Olin GrahamSenate Republicans face tough decision on replacing Ginsburg Democratic senator calls for eliminating filibuster, expanding Supreme Court if GOP fills vacancy What Senate Republicans have said about election-year Supreme Court vacancies MORE (R-S.C.) and Cory Booker Cory Anthony BookerBipartisan praise pours in after Ginsburg's death DHS opens probe into allegations at Georgia ICE facility Democratic lawmakers call for an investigation into allegations of medical neglect at Georgia ICE facility MORE (D-N.J.), would require a judge to approve a Justice Department request to fire Mueller or any other special counsel.

A second bill, from Sen. Thom Tillis Thomas (Thom) Roland TillisWhat Senate Republicans have said about election-year Supreme Court vacancies Chamber of Commerce endorses McSally for reelection Airline job cuts loom in battleground states MORE (R-N.C.) and Sen. Chris Coons Christopher (Chris) Andrew CoonsBiden promises Democratic senators help in battleground states Shakespeare Theatre Company goes virtual for 'Will on the Hill...or Won't They?' The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Pence lauds Harris as 'experienced debater'; Trump, Biden diverge over debate prep MORE (D-Del.), would let Mueller or any special counsel challenge their firing in court.



But following the news of the indictments, Republicans pushed back on Democrats calling for legislation to protect Mueller, saying it wasn’t necessary.

"I don’t feel an urgent need to pass that law until you show me that Mr. Mueller is in jeopardy," Graham said Monday, adding that no one in their “right mind” would fire Mueller.