Sen. Orrin Hatch Orrin Grant HatchBottom line Bottom line Senate GOP divided over whether they'd fill Supreme Court vacancy MORE (R-Utah) is offering support to special counsel Robert Mueller after he announced charges against Paul Manafort, President Trump's former campaign chairman.

"There will be procedural milestones, like today’s announcement, along the way, but that doesn’t change the basic equation that the Special Counsel needs the time and support necessary to get to the bottom of things," Hatch said in a statement.

He added it's "in the best interest for all parties involved to allow Bob Mueller to conduct a full and vigorous investigation."

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Mueller announced charges against Manafort and Manafort's former business associate Richard Gates on Monday. Both pleaded not guilty.

Democrats are using the news to double down on their push to get Congress to pass legislation limiting the Trump administration's ability to fire Mueller unilaterally.

But Republicans have largely been mum on the development.

Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellGraham: GOP will confirm Trump's Supreme Court nominee before the election Trump puts Supreme Court fight at center of Ohio rally The Memo: Dems face balancing act on SCOTUS fight MORE (R-Ky.) has yet to comment. He didn't mention Manafort or Mueller during his opening speech on Monday afternoon and left a press conference on judicial nominees before the question-and-answer portion.

When reporters during the press conference began asking questions about Manafort, Senate Judiciary Committee Chairman Chuck Grassley Charles (Chuck) Ernest GrassleyGardner signals support for taking up Supreme Court nominee this year Grassley, Ernst pledge to 'evaluate' Trump's Supreme Court nominee McConnell digs in on vow to fill Ginsburg's Supreme Court seat MORE (R-Iowa), who said earlier Monday that Mueller should be allowed to do his job, turned and exited the press conference using a door behind him.

And when Sen. John Cornyn John CornynTumultuous court battle upends fight for Senate Texas Democrats roll out first wave of planned digital ads as Election Day nears Calls grow for Biden to expand election map in final sprint MORE (R-Texas) asked if any reporters had any on-topic questions, a reporter quipped: "I have a question about a different Catholic, named Paul Manafort."

Cornyn separately told reporters earlier Monday that the "special counsel's got his own responsibilities and it doesn't involve us."

"I think he knows what to do and he's doing it," he said, asked about legislation to "shield" Mueller from the president.