WASHINGTON — Republican congressional leaders on Monday broke their silence about the participation of two House Republicans at a far-right conference with ties to white supremacy, denouncing the actions of Representative Marjorie Taylor Greene of Georgia and Representative Paul Gosar of Arizona.

Three days after Ms. Greene appeared in person and Mr. Gosar by video at the America First Political Action Conference, organized by a prominent white supremacist, Nick Fuentes, the responses reflected mounting pressure on top Republicans to denounce extremists in their ranks.

They followed a sharp condemnation by the Republican Jewish Coalition and a more oblique one by the Republican National Committee, and marked a rare public rebuke by G.O.P. congressional leaders, who have more often stayed mum in response to outrageous language and conduct by their hard-right members.

By Monday afternoon, Representative Kevin McCarthy of California, the minority leader who aspires to be speaker, told reporters at the Capitol that he found the pair’s behavior “appalling and wrong.”

After taking Republicans to Israel and the hallowed museum of the Holocaust, Yad Vashem, Mr. McCarthy said, he had returned to Washington to find that two colleagues “went and participated with a group that has a leader that many times gives antisemitic views, and led a chant for Putin.”

“The party should not be associated any time, any place with somebody who is antisemitic,” he added, calling Ms. Greene’s failure to leave the stage after Mr. Fuentes praised Adolf Hitler “unacceptable.”

His comments came not long after Senator Mitch McConnell of Kentucky, the top Senate Republican, released a statement saying, “There’s no place in the Republican Party for white supremacists or antisemitism.”

Ms. Greene has rejected criticism of her participation, at first saying that she did not know who Mr. Fuentes was. But on Sunday, she issued a rambling, defiant broadside that edged into antisemitism when she decried her attackers as “the Pharisees in the Republican Party,” referring to an ancient group of Jewish leaders whom Jesus called hypocrites.

“We’re not going to be deterred by journalists and Washington insiders who fear the name of our Lord, and relentlessly attack those of us who proclaim his name,” Ms. Greene said. “We know that Christ is our only judge.”

The episode was yet another indication of the extremism problem Republicans face within their ranks, during what should be heady days for the party. President Biden’s abysmal approval ratings have buoyed its fortunes and put control of Congress within its grasp after the midterm elections in November. But the words and actions of prominent Republicans, including former President Donald J. Trump, the G.O.P.’s nominal leader, have kept lawmakers and leaders on the defensive.

Mr. Trump has repeatedly praised Russian President Vladimir V. Putin in recent days as “savvy,” “a genius” and “smart,” resurrecting questions over the former president’s efforts to withhold military aid from Ukraine to force its president, Volodymyr Zelensky, to dig up dirt on Mr. Trump’s Democratic rival, Joseph R. Biden Jr.

“This was Zelensky, now a world hero, asking for weapons, and it was an American president slow-walking the provision of those weapons in order to have Zelensky carry out a political investigation on his foe,” Senator Mitt Romney of Utah, the only Republican to vote for Mr. Trump’s conviction after his first impeachment, said Sunday on CNN’s “State of the Union.” “It was wrong. It was in violation of a president’s responsibility to defend our nation and defend the cause of freedom.”

Pressed on ABC’s “This Week” to repudiate Mr. Trump’s praise for Mr. Putin, Senator Tom Cotton, Republican of Arkansas, snapped, “If you want to know what Donald Trump thinks about Vladimir Putin or any other topic, I’d encourage you to invite him on your show.”

But neither Ms. Greene nor Mr. Gosar is a party leader. The House stripped Ms. Greene of her committee assignments for threats to Democratic members, and formally censured Mr. Gosar for posting a cartoon depicting him slashing the neck of Representative Alexandria Ocasio-Cortez, Democrat of New York, before violently confronting Mr. Biden.

Mr. McCarthy meted out no punishment in either case. The only House Republicans who have faced penalties for their words or deeds have been Representative Liz Cheney of Wyoming and Adam Kinzinger of Illinois, who were censured by the party this month for participating in the investigation of the Jan. 6, 2021 attack on the Capitol, which the R.N.C. called “persecution of ordinary people engaged in legitimate political discourse.”

Mr. McCarthy defended the censure, while Mr. McConnell repudiated it.

In the case of Ms. Green and Mr. Gosar, the Republican Jewish Coalition, which is generously funded by powerful party donors, swiftly denounced their appearances last week at the America First conference, where the lawmakers shared a stage with Mr. Fuentes, an antisemitic Holocaust denier who questioned why comparing Mr. Putin to Hitler was “a bad thing.”

The crowd at the conference — which was running at the fringes of the larger Conservative Political Action Conference, or CPAC — could be heard on videos chanting “Putin, Putin.”

“It is appalling and outrageous that a member of Congress would share a platform with an individual who has actively spread antisemitic bile, mocked the Holocaust, and promoted dangerous anti-Israel conspiracy theories,” the Republican Jewish group stated, adding, “This has absolutely no place in the Republican Party, and R.J.C. will actively oppose anyone who associates with Nick Fuentes, AFPAC, and their ilk.”

Without naming any members, the Republican National Committee chairwoman, Ronna McDaniel, said on Sunday that “white supremacy, neo-Nazism, hate speech and bigotry are disgusting and do not have a home in the Republican Party.”

Mr. Fuentes, for his part, used the flap to promote his own gathering.

“After a day of vicious attacks against Marjorie Taylor Greene for speaking at AFPAC last night, Donald Trump gives her a shout-out and endorsement from the main stage at CPAC,” he wrote on his Telegram account, before suggesting that Mr. Trump would attend in the future.

Kenneth S. Stern, director of the Bard Center for the Study of Hate at Bard College, said the moment was reminiscent of the late 1980s and early 1990s when David Duke, a former Ku Klux Klan leader, was making inroads into the Republican Party and trying to push his ideas into the mainstream.

In 1991, President George H.W. Bush called a news conference to denounce Mr. Duke as a “charlatan” who did not deserve “one iota of public trust.”

“When someone has so recently endorsed Nazism, it is inconceivable that someone can reasonably aspire to a leadership role in a free society,” he said.

In this case, Mr. Stern said, “I’m less worried about Marjorie Taylor Greene showing up at a conference with people she should be embarrassed to be with and more concerned with the failure of a lot of people in the Republican Party to call out the Big Lie with Donald Trump and the 2020 election.”

For Republicans, the issue is sensitive. Ms. Greene said she would not be silenced when she is addressing the youthful activists who should be groomed into the next generation of Republican voters.

“We must tutor our youth in the ways of righteousness so they do not stray into darkness,” she said.

And the energy on the far right is young, led by Mr. Fuentes and his “groypers,” who have tempered their racist language as they aim to take their ideas of white nationalism into the mainstream.

It is also not at all clear that Republicans would pay a price for the actions on their right.

“I have absolute confidence in Kevin McCarthy,” said Matt Brooks, the executive director of the Republican Jewish Coalition. “He’s rock solid when it comes to this. If he wants to deal with the issue publicly or privately, all I can tell you is, it will be dealt with. It’s not something he will ignore.”

Ari Fleischer, a former White House press secretary and prominent Jewish Republican, called Ms. Greene’s appearance “as wrong as wrong gets” and “a moral line that should never be crossed.”

But he, too, expressed confidence in Mr. McCarthy.

“They went, it’s their behavior,” he said. “I have 100 percent confidence in Kevin and Republican leadership that, whether in public or in private, they’re handling it well.”