WASHINGTON — Representative Kevin McCarthy’s denial of disparaging comments he made about President Donald J. Trump after the Capitol attack on Jan. 6, 2021, exposed a widely known but seldom seen phenomenon in Washington: the hypocrisy of Republicans who have privately scorned Mr. Trump while publicly defending him.

Mr. McCarthy, the California Republican who is campaigning to be speaker of the House if his party wins the majority in November, had dismissed as “totally false and wrong” a report that he had told fellow G.O.P. leaders he would urge Mr. Trump to resign from office after the riot. But an audio recording of the conversation revealed Mr. McCarthy’s denial to be a lie.

For Mr. McCarthy, the immediate political problem was not being caught in a lie. In the Republican Party, which has coalesced around Mr. Trump’s claim that the 2020 election was stolen from him, falsehoods have become routine and even accepted.

The greater danger for Mr. McCarthy on Friday was the truth — that, with the disclosure of his negative comments about Mr. Trump, he might invite the ire of the former president, who maintains a stranglehold on his party and on a powerful faction of extremist House members who already pose the greatest risk to his political future.

For a Republican leader who has prostrated himself before Mr. Trump in ways large and small — including famously sorting through a package of Starburst candies to present him with only his favorite red and pink chews — the lie was his latest show of loyalty.

Some of Mr. Trump’s fiercest defenders on Capitol Hill have long criticized the former president and his family members behind closed doors, venting about his erratic policy decisions and tweets while expressing their total fealty in public. The release of the audio of Mr. McCarthy’s comments was a rare moment where the duplicity was on public display.

Mr. McCarthy spent Friday morning working the phones, calling members of his conference to gauge their level of concern about the recording. A source familiar with the conversations said his team had also been asking rank-and-file members to post tweets supporting Mr. McCarthy for speaker.

“Republicans are going to take back the majority in November and when we do, Kevin McCarthy will be our Speaker,” Representative Ashley Hinson, Republican of Iowa, tweeted on Friday.

Advisers to Mr. Trump said that he was unlikely to turn against Mr. McCarthy and that the two had spoken on Thursday morning, after the story became public, and had what they called “a good conversation.”

Another person familiar with the talks said that the two spoke again on Thursday night, after the audio was released showing that Mr. McCarthy’s denial had been a lie, and that Mr. Trump did not appear to be rattled by the statements.

Mr. McCarthy’s prime concern on Friday, according to a person familiar with the situation, was about Republicans he thought would be upset by his private criticism of Mr. Trump — not those who might be alarmed by the fact that he had been exposed as a liar in denying it.

There were few expressions of outrage from Republican members of Congress about their leader — one who would be in line to succeed the president if he achieves his aspiration of being speaker of the House — having been caught in a falsehood. They appeared to be following the lead of Mr. Trump.

The former president “probably realizes this is all being driven by the left and the mainstream media,” said Jason Miller, an adviser to Mr. Trump, noting that it would work in Mr. McCarthy’s favor that the recording was first aired on an MSNBC broadcast hosted by Rachel Maddow, a frequent target of the right. “The speaker battle will happen after we win back the majority.”

Mr. McCarthy’s private expressions of outrage most likely did not come as any surprise to Mr. Trump, who was irate when the congressman criticized him immediately after the Capitol assault in an unusually sharp House floor speech, saying he “bears responsibility” for the riot and proposing that he be censured.

But Mr. McCarthy soon changed his tune after visiting the former president at his resort in Palm Beach, Fla. He walked back his condemnations, ultimately fought the creation of an inquiry and led an effort to purge Representative Liz Cheney, Republican of Wyoming, from her House leadership post for speaking out against Mr. Trump.

Some Republican lawmakers privately downplayed the significance of the taped conversation. They noted that Mr. McCarthy was not known as a truth-teller or someone who has been deeply loyal to Mr. Trump. Rather, he has built his reputation as a political operator whose approach is to fall in line with where a majority of his conference is heading.

The recording, those members said, merely revealed Mr. McCarthy for the person his conference knew him to be. And for now, there was no obvious alternative to challenge him in a race for speaker.

But Mr. McCarthy is also up against powerful political enemies who hold sway with the extremists in his conference. On Friday morning, Stephen K. Bannon, the former top White House adviser, said on his popular podcast that it was a “cardinal sin” to deny comments that were then aired on tape.

In his quest to become speaker, Mr. McCarthy has long engaged in painful contortions to please the disparate factions of his conference — all of whose support he will need to become the most powerful Republican in Washington.

That has often meant going out of his way not to antagonize Mr. Trump or his staunchest allies in Congress. He has dodged reporters in the hallways of the Capitol asking him about a Republican National Committee resolution that suggested that Jan. 6 was “legitimate political discourse” and censured members of his conference for participating in the House investigation of the attack. He has refrained from punishing far-right Republicans who have attended white supremacist rallies or released videos promoting violence against Democrats, instead saying that he has had stern, private conversations with them about their behavior.

Mr. McCarthy’s office did not respond to requests for comment on Friday about the tape. He is scheduled to travel on Monday with a group of House Republicans to the southwestern border in Texas, where he is expected to hold a news conference and is likely to be pressed to publicly respond to the taped conversation.

In Mr. Trump’s circles, Mr. McCarthy is already viewed with skepticism and little trust. The relationship between the two men, aides to Mr. Trump said, was cordial but not particularly close. The former president is closer with House members like Representative Elise Stefanik of New York and Representative Jim Jordan of Ohio, both of whom he speaks to regularly and views as loyalists. Mr. McCarthy, in contrast, often relies on his aide Brian Jack, a former White House political director, as an intermediary who has a solid relationship with the former president.

Representative Matt Gaetz, Republican of Florida and a critic of Mr. McCarthy’s who has pushed for Mr. Trump to become speaker, was the first to denounce his comments.

“While I was rallying in Wyoming against Liz Cheney… Kevin McCarthy was defending Liz Cheney among House Republicans,” Mr. Gaetz posted on Twitter on Friday, noting that Mr. McCarthy “should have trusted my instincts, not your own.”

Representative Adam Kinzinger, Republican of Illinois and a vocal critic of Mr. Trump, tweeted that Mr. McCarthy should be “ashamed” of his lie. “Republicans, your leaders think you are dumb,” Mr. Kinzinger wrote. “Let’s be done with them.”