Republicans say President Trump Donald John TrumpBiden leads Trump by 36 points nationally among Latinos: poll Trump dismisses climate change role in fires, says Newsom needs to manage forest better Jimmy Kimmel hits Trump for rallies while hosting Emmy Awards MORE would be making a big mistake in firing Deputy Attorney General Rod Rosenstein Rod RosensteinDOJ kept investigators from completing probe of Trump ties to Russia: report Five takeaways from final Senate Intel Russia report FBI officials hid copies of Russia probe documents fearing Trump interference: book MORE.

The Justice Department’s No. 2 official has been in the president’s crosshairs since appointing special counsel Robert Mueller Robert (Bob) MuellerCNN's Toobin warns McCabe is in 'perilous condition' with emboldened Trump CNN anchor rips Trump over Stone while evoking Clinton-Lynch tarmac meeting The Hill's 12:30 Report: New Hampshire fallout MORE to lead the agency’s Russia investigation.

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He’s the only official who could fire Mueller given Attorney General Jeff Sessions Jefferson (Jeff) Beauregard SessionsGOP set to release controversial Biden report Trump's policies on refugees are as simple as ABCs Ocasio-Cortez, Velázquez call for convention to decide Puerto Rico status MORE’s decision to recuse himself from Russia-related matters.

Some Republicans are now worried that a soon-to-be-released memo from GOP staff on the House Intelligence Committee could hand Trump more ammunition to fire Rosenstein — a move they fear would boomerang on the White House and Republicans running for reelection in the House and Senate.

Removing Rosenstein “raises more flags than it dismisses,” said Rep. Mark Sanford Mark SanfordOn The Money: Business world braces for blue sweep | Federal Reserve chief to outline plans for inflation, economy | Meadows 'not optimistic' about stalemate on coronavirus deal Trump critic Sanford forms anti-debt advocacy group Republicans officially renominate Trump for president MORE (S.C.), one of several Republicans who told The Hill on the record that Trump should not fire the deputy attorney general.

Ousting Rosenstein would only make Trump look guilty, according to Sanford.

“That’s why a whole host of folks inside and outside the White House have warned against that kind of thing,” he said.

“I’m a fan of letting the process run its course,” said Rep. David Joyce David Patrick JoyceRepublicans shrug off Kasich's Democratic convention speech The Hill's Morning Report - Presented by The American Investment Council - Trump takes his 'ready to reopen' mantra on the road GE cutting up to one-quarter of aviation unit's workers MORE (R-Ohio), a former county prosecutor. “I think we should let Rosenstein, Mueller and everybody else do their jobs and wait to see what the outcome is.”

“I would advise [Trump] not to do that and I don’t think he will,” added Rep. Gus Bilirakis (R-Fla.), an attorney.

“Bad idea,” Sen. Jeff Flake Jeffrey (Jeff) Lane FlakeJeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Republican former Michigan governor says he's voting for Biden Maybe they just don't like cowboys: The president is successful, some just don't like his style MORE (R-Ariz.), who has frequently clashed with Trump, chimed in. “It was a bad idea to fire [former FBI Director James] Comey. I think he recognizes that by now, because that’s what got him Mueller. And this would [lead to] just trouble.”

Most GOP lawmakers are in favor of making the House Intelligence Committee memo public, arguing that doing so would let Americans make up their own minds on whether the FBI went too far in seeking surveillance warrants related to the probe of Russia’s involvement in the 2016 presidential election.

The memo, which the committee voted on Monday night to make public along party lines, has been sent to the White House, which has five days to decide whether to allow its release. It is believed to report that Rosenstein gave the green light to continue surveillance of Trump campaign official Carter Page last spring. Democrats on the panel argue it is little more than a set of cherry-picked GOP talking points and have produced their own memo, though the committee voted against making it public.

Speaker Paul Ryan Paul Davis RyanKenosha will be a good bellwether in 2020 At indoor rally, Pence says election runs through Wisconsin Juan Williams: Breaking down the debates MORE (R-Wis.) was prepared with notes to answer questions about the memo and Rosenstein at his press conference on Tuesday, and was quick to walk a careful line.

Asked about Trump’s private grumblings about Rosenstein, he defended the Justice official, saying he was doing a “fine job” and that he saw “no reason” why Trump should fire him.

The Speaker also noted that Rosenstein, who served as U.S. attorney for Maryland under Presidents George W. Bush and Obama, was appointed deputy attorney general after the 2016 election.

But Ryan offered support for Republicans on the Intelligence panel and criticism of the FBI, saying it was up to the Department of Justice and FBI to “clean their own house” if they have personnel problems.

The Intelligence memo criticizes the department and the FBI for failing to adequately explain to a secret spy court that some of the information included in a surveillance application for Page came from opposition research paid for in part by Democratic presidential candidate Hillary Clinton Hillary Diane Rodham ClintonBiden leads Trump by 36 points nationally among Latinos: poll Democratic super PAC to hit Trump in battleground states over coronavirus deaths Battle lines drawn on precedent in Supreme Court fight MORE.

The Republican warnings that Trump not fire Rosenstein come a day after FBI Deputy Director Andrew McCabe, whom Trump openly accused of being biased against him, announced he would step down weeks earlier than had been expected.

McCabe had been Comey’s top deputy before Trump fired Comey last May as he investigated possible collusion between Russia and the Trump campaign.

In a brief interview Tuesday, House Intelligence Committee Chairman Devin Nunes Devin Gerald NunesSunday shows preview: Justice Ginsburg dies, sparking partisan battle over vacancy before election Sunday shows preview: With less than two months to go, race for the White House heats up Sunday shows preview: Republicans gear up for national convention, USPS debate continues in Washington MORE (R-Calif.) said he had “no idea” and “no knowledge” of any plans by Trump to fire Rosenstein.

Top Trump allies on Capitol Hill did not explicitly call for Rosenstein’s ouster on Tuesday. House Freedom Caucus Chairman Mark Meadows Mark Randall MeadowsAirline CEOs plead with Washington as layoffs loom Trump reacts to Ginsburg's death: 'An amazing woman who led an amazing life' Trump carries on with rally, unaware of Ginsburg's death MORE (R-N.C.) declined to comment for this story. But Rep. Jim Jordan James (Jim) Daniel JordanSunday shows preview: Justice Ginsburg dies, sparking partisan battle over vacancy before election House passes resolution condemning anti-Asian discrimination relating to coronavirus Republicans call for Judiciary hearing into unrest in cities run by Democrats MORE (R-Ohio), a former head of the Freedom Caucus, suggested Rosenstein was less than forthcoming when he questioned him at a recent hearing about potential anti-Trump bias at the Justice Department.

During that House Judiciary Committee hearing last month, Rosenstein stood by Mueller and said he would not fire him without good cause.

“I didn’t feel like his answers were all that great on the committee,” Jordan told The Hill on Tuesday. “That was my one interaction with him, and I wasn’t too impressed.”

Trump had considered firing Rosenstein last summer, The New York Times reported. Instead, he ordered White House counsel Don McGahn to fire Mueller, but the president backed down after McGahn threatened to quit.

There is speculation on Capitol Hill that if Trump got rid of Rosenstein, he could replace him with a political ally who would fire Mueller and stop the federal Russia probe, which now includes whether Trump committed obstruction of justice.

But some top legal minds in the GOP are warning fellow Republicans to back off. House Oversight and Government Reform Committee Chairman Trey Gowdy Harold (Trey) Watson GowdySunday shows preview: Election integrity dominates as Nov. 3 nears Tim Scott invokes Breonna Taylor, George Floyd in Trump convention speech Sunday shows preview: Republicans gear up for national convention, USPS debate continues in Washington MORE (R-S.C.) said on “Fox News Sunday” that he has “100 percent” confidence in Mueller to conduct a fair investigation and urged his colleagues to “leave him the hell alone.”

“I’d follow the good advice of Trey Gowdy of keeping Mueller. Let him do his thing,” said Rep. Tim Walberg Timothy (Tim) Lee WalbergThe health care crisis no one is talking about Overnight Defense: Pentagon policy chief resigns at Trump's request | Trump wishes official 'well in his future endeavors' | Armed Services chair warns against Africa drawdown after trip GOP chairman after Africa trip: US military drawdown would have 'real and lasting negative consequences' MORE (R-Mich.). “I think if you do any type of firing, you just resurrect all the partisan stuff.”

One frequent GOP Trump critic, Rep. Walter Jones Walter Beaman JonesExperts warn Georgia's new electronic voting machines vulnerable to potential intrusions, malfunctions Georgia restores 22,000 voter registrations after purge Stacey Abrams group files emergency motion to stop Georgia voting roll purge MORE (N.C.), said it’d be foolish to try to halt the Mueller probe given that it’s now in the “fourth quarter.”

“Mueller is doing the people’s work, Rosenstein selected him, and I think if you have nothing to hide, them you would want to encourage them to complete the job,” Jones told The Hill. “When you start terminating those for doing their job, there’s something wrong.”

Firing Rosenstein now, Jones said, “would create a national concern by a lot of people.”

Katie Bo Williams contributed.