Speaking as voters in 13 states cast their ballots on Super Tuesday, House Speaker Paul Ryan said potential Republican presidential nominees must reject any group "built on bigotry." (Reuters)

House Speaker Paul D. Ryan (R-Wis.) issued a stern rebuke Tuesday to his party’s presidential front-runner, calling Donald Trump’s recent equivocation about receiving support from white supremacists a “fundamental” break from conservative orthodoxy.

“This party does not prey on people’s prejudices,” Ryan told reporters at the weekly House GOP leadership news conference.

Without addressing Trump by name, Ryan noted that the Republican presidential campaign had veered into topics such as views on “white supremacists” that should prompt “no evasion” of the topic other than repudiation of those values.

It was a clear reference to Trump’s recent comments and actions in which he has said that he needs to further study the views of David Duke, a former Ku Klux Klan leader from Louisiana who has encouraged listeners of his talk show to back Trump, as well as to social-media comments and tweets that seem to endorse the views of known racists.

“When I see something that runs counter to who we are as a party and as a country, I will speak up, so today I want to be very clear about something,” Ryan said. “If a person wants to be the nominee of the Republican Party, there can be no evasion and no games. They must reject any group or cause that is built on bigotry. This party does not prey on people’s prejudices. We appeal to their highest ideals. This is the party of Lincoln.”

He added: “This is fundamental. And if someone wants to be our nominee, they must understand this. I hope this is the last time I need to speak out on this race.”

[Donald Trump and David Duke: For the record]

Senate Majority Leader Mitch McConnell (R-Ky.) joined in the condemnations Tuesday afternoon after exiting a party luncheon. He did not reference Trump by name, but denounced “one of our presidential candidates and his seeming ambivalence about David Duke and the KKK.”

“Let me make it perfectly clear: Senate Republicans condemn David Duke, the KKK, and his racism,” McConnell said. “That is not the view of Republicans that have been elected to the United States Senate, and I condemn his comments in the most forceful way.”

The remarks by Ryan and McConnell came on the biggest day of the primary season, as Trump is expected to win an overwhelming share of delegates in 11 states where ballots are cast. By the time last votes are counted, he could win 13 of the first 15 states that have held primaries or caucuses, putting him on a path toward the nomination that some lawmakers said was hard to stop.

[Super Tuesday: Voters head to the polls, but not all are pleased by the choices]

On Tuesday morning, Trump tried to be slightly more forceful in his comments on Duke. In a phone interview on ABC’s “Good Morning America,” he was asked whether he categorically rejects the support of all white supremacists. “Of course I am,” he responded. “Of course I am.”

Here's what Republican presidential candidate Donald Trump has said about white supremacist David Duke in several interviews in the past 15 years. (Sarah Parnass/The Washington Post)

Across the Senate and House this week, a broad sense of despair settled in among most rank-and-file Republicans that Trump is stampeding toward the nomination. Ryan has not endorsed another candidate in the race, nor has McConnell.

The Senate leader paid a rare visit Tuesday morning to Ryan’s House caucus, and the issue of the presidential campaign never came up, according to lawmakers leaving the huddle. McConnell talked about his opposition to moving forward with President Obama’s Supreme Court nominee to replace the late Associate Justice Antonin Scalia, and rank-and-file lawmakers asked questions about the budget process.

David Duke has a long history in politics and the white supremacy movement. Here are key moments in Duke's life in the public eye. (Claritza Jimenez/The Washington Post)

Social conservatives are among the most distraught Republicans inside the Capitol, wary of Trump’s long record of supporting Democrats who favor abortion rights and gay marriage.

“It’s not time to raise the white flag just yet. But there’s a moment in the life of every problem like this, when it’s big enough for reasonable people to see and still small enough to be addressed. That window is closing,” Rep. Trent Franks (R-Ariz.), one of the leading antiabortion lawmakers, said after Tuesday’s meeting.

Franks is unaligned in terms of the presidential race. Like many prominent Republicans, including Ryan, Franks said Tuesday that he would support Trump as the nominee — but only because he cannot stand the Democratic front-runner, Hillary Clinton.

“If it comes down to a vote between Hillary Clinton and Donald Trump, the equation is simple: Conservatives cannot trust Donald Trump to do the right thing, but we can definitely trust Hillary Clinton to do the wrong thing, so I will vote for Donald Trump,” he said.

Ryan also said he would support the person Republican voters select as their nominee.

“I plan to support the nominee,” Ryan said. “I think I’ve said enough this morning about what’s happening right now. My plan is to support the nominee.”

McConnell has previously said he would support the Republican presidential nominee, and he did not revise that stance under questioning Tuesday: “Beyond what I just said, I’m going to continue to avoid weighing in on the presidential contest at this point.”

He was asked about a New York Times report published over the weekend indicating that he had privately told his Senate colleagues that GOP senators would drop Trump “like a hot rock” were he to become the presidential nominee.

“I don’t remember saying anything like that to all of you,” McConnell said.

After he was pressed by a reporter, he changed his emphasis slightly: “I don’t remember saying anything like that to all of you.”

Given this dejected state, some Republicans are hoping to rally conservatives around Sen. Marco Rubio (R-Fla.) as the alternative to Trump. So far 57 congressional Republicans have backed Rubio, according to the Hill newspaper’s tally, which is easily the largest haul inside the Capitol.

However, the groundswell for Rubio has hit limits and there are questions about whether his appeal is broad enough. Perhaps most emblematic of that is the non-endorsement of Sen. Bob Corker (R-Tenn.).

Corker has served on the Foreign Relations Committee the past five years with Rubio, the past three as the most senior Republican on the panel. In debates and on the stump, Rubio cites his work on that committee as evidence of his readiness to handle global affairs in the Oval Office.

On Monday evening, Corker refused to reveal whom he voted for in Tuesday’s Tennessee primary. “My wife doesn’t even know whom I voted for,” he said.

Corker’s internationalist world view clashes sharply with Trump’s protectionist positions, and the senator has also publicly clashed with Sen. Ted Cruz (R-Tex.), a Republican presidential candidate, on many issues, leaving almost no one other than Rubio who shares similar policy positions. “We have a lot of people throughout the state that have worked hard for various candidates. And I just thought early on that I would probably not endorse,” Corker said.

Another mainstream conservative, Sen. John Hoeven (R-N.D.), whose views put him against Trump and Cruz, said he was not prepared to endorse. “I do like Marco, yeah, you know, I’ve said that all along. But at this point I’m going to just go with our nominee, let Republicans make that call,” he said.  “We’ve got a ways to go yet, this is yet to be decided.”

Trump’s rise has also thrown off Rubio’s supporters regarding the “#nevertrump” campaign that he is promoting online. While some Republicans have declared they would not support Trump, others aren’t willing to say that yet.

“I am a ‘Never Hillary’ person, that is the only position I have taken on a ‘never.’ We’ll see how the rest of this plays out. I am strongly pro-Marco Rubio,” Sen. Jim Risch (R-Idaho) said.

Sen. Deb Fischer (R-Neb.), who supports Rubio, rejected having a conservative run as an independent if Trump wins the nomination.

“I think a third option would give the White House to Hillary Clinton, and I’m not about to do that. Her first action as president would be to nominate a liberal progressive Supreme Court justice, that’s what’s at stake here, and we can’t forget that,” she said.

Mike DeBonis contributed to this report. 

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