WASHINGTON — House Republicans have tried to chip away at the credibility of Robert S. Mueller III’s inquiry into Russia’s 2016 election interference since shortly after it began, savaging members of his investigative team as “angry Democrats,” and calling into question his impartiality.
But as they prepare to meet Mr. Mueller, the former special counsel, face to face on Wednesday at two high-stakes congressional hearings, some of the Republican Party’s loudest voices are urging caution against an aggressive confrontation. Victory, they say, could come with a light touch as much as pointed questioning.
“The obvious first question will be, ‘When did you know there was no coordination and no conspiracy?’” said Representative Jim Jordan of Ohio, one of the Republicans’ most recognizable attack dogs. He now sees Mr. Mueller as the ideal mouthpiece to deliver the conclusion that the investigation found insufficient evidence to charge anyone with conspiring with Russia to influence the 2016 election.
Not every Republican is on board with a gentler approach. Representative Louie Gohmert of Texas rejected any suggestion he might pull his punches. “I can’t wait,” he said. Representative Matt Gaetz, a firebrand from Florida, pledged a pointed discussion of bias, which he has long maintained corrupted the investigation.
His goal for the hearing? “We are going to re-elect the president,” he said.
But with public opinion tilted against impeachment and Democrats’ investigations plodding along, many Republicans on the House Judiciary and Intelligence Committees are contemplating a “do no harm” approach rather than putting a match to Mr. Mueller’s image. Better to try to look reasonable next to committee Democrats, who they believe will struggle to knock Mr. Mueller off his conclusions.
“He exonerated the president on the collusion issue and for anybody to go after him would seem silly to me,” said Representative Ken Buck, Republican of Colorado.
The strategy reflects two assumptions about Mr. Mueller’s appearance shared by lawmakers from both parties: first, that he will not take the bait to answer questions beyond the contents of his written report, and second, that his testimony before the House committees could be one of the most closely watched congressional performances in decades. For both parties, the hearings present an unusual chance to shape the views of a large number of Americans who have not read Mr. Mueller’s 448-page report, which was released in April.
The report did identify at least 10 episodes that could be construed as obstruction of justice, and Mr. Mueller pointedly declined to exonerate Mr. Trump. But he did not refer the president for prosecution either.
For Republicans, the hearings mean introducing a new audience to passages of the report more favorable to Mr. Trump, as well as to accusations that have become accepted truth on the right: Mr. Trump was the target of an unfair and rules-breaking investigation by law enforcement officials intent on upending first his campaign, then his presidency.
They are likely to question Mr. Mueller about inflammatory anti-Trump texts exchanged by two F.B.I. officials, Peter Strzok and Lisa Page, who helped start the bureau’s investigation of the Trump campaign and later joined Mr. Mueller’s team before the messages were discovered. Republicans intend to ask Mr. Mueller about the F.B.I.’s use of a salacious but unverified dossier of Trump-Russia connections to obtain a surveillance warrant on a former Trump campaign aide in 2016.
And they want to know why Mr. Mueller deviated from Justice Department regulations governing his work in declining to reach a decision on obstruction of justice but included unflattering information on Mr. Trump anyway.
What many Republicans want to try to avoid is making matters personal — the fewer “witch hunts” and incendiary accusations of a coup d’état by the so-called deep state, the better.
Representative Doug Collins of Georgia, the top Republican on the Judiciary Committee, promised “honest, pointed straightforward” questions for the special counsel but paused at the word “aggressive.”
Others cautioned against spending too much time fishing for Mr. Mueller to validate their concerns when he is unlikely to engage, or worse, could offer a convincing defense of his team.
“To me, it is not a question about whether or not we need those answers; it is whether this will be the proper forum or not,” said Representative Mike Johnson, Republican of Louisiana. “Strategically, can we get Mr. Mueller to address those issues in this forum? I have some doubts about that.”
Republican lawmakers and aides stressed that their approach to the questioning was still in flux and could shift based on Mr. Mueller’s responsiveness. Democrats negotiated both sessions directly with Mr. Mueller’s associates, and though Republicans have mostly supported calling Mr. Mueller, they have had little role in determining the length of his appearances or the procedures governing the hearings.
At least one question appears to be settled: Given the limited time for questioning, several people involved in the Republican strategy sessions said it was unlikely they would try to deploy parliamentary high jinks of the sort often used by the minority party to run out the clock. Better to fight it out on the merits, they have reasoned.
The rest, it seems, may be sorted out in real time between more temperamentally moderate members and firebrands like Mr. Gaetz and Mr. Gohmert.
“The quicker this all goes away the better,” said Representative Mike Conaway, Republican of Texas, who played a key role in leading the Intelligence Committee’s own Russia investigation last term. “People are weary of it. When I talk to people back home, the independents are weary about this.”
Representative Chris Stewart, Republican of Utah on the Intelligence Committee, said he wanted to ask Mr. Mueller if he was aware of the political views of investigators on his team when he hired them. As for ad hominem attacks, he said, “I don’t think it benefits anyone.”
Julian Epstein, who was the chief counsel to Democrats on the House Judiciary Committee during President Bill Clinton’s impeachment, said his party took a two-toned approach to questioning the independent counsel in that case, Ken Starr, and found it worked well.
“We had the bomb-thrower caucus and the moderate caucus — and both played usefully to different audiences,” he said.
In this case, he said, Republicans needed only to play defense and “maintain the public opinion status quo.”
“The Republican playbook is pretty obvious,” Mr. Epstein said. “All they have to say is, ‘Mr. Mueller, can you repeat again that you believe there was no underlying criminal conspiracy by the Trump campaign on Russian interference? And did you say that while a reasonable prosecutor could prosecute on obstruction, a reasonable prosecutor might also decline to prosecute?’”
Republicans have been drawing up a litany of other questions to put to Mr. Mueller.
Mr. Stewart suggested that the Intelligence Committee would take aim at the F.B.I.’s use of the dossier — an uncorroborated document drafted by a former British spy and funded in part by Democrats — to obtain a secret Foreign Intelligence Surveillance Act warrant to spy on a Trump campaign associate, Carter Page, after he left the campaign in 2016. Republicans say that action was an abuse of power by senior law enforcement officials intent on targeting Mr. Trump’s campaign.
“They are questions that deserve answers,” Mr. Stewart said. “The whole FISA process is extraordinarily concerning to me.”