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.