Republican leaders moved forcefully on Tuesday to control the damage from a pair of scandals that have suddenly disrupted the party as it prepares to take full control on Capitol Hill.

In back-to-back moves, House Speaker John A. Boehner (R-Ohio) pushed out Rep. Michael G. Grimm (R-N.Y.), who pleaded guilty last week to federal tax-evasion charges, and backed Majority Whip Steve Scalise (R-La.), who acknowledged that he once ­addressed a white-supremacist group before coming to Congress.

Some Republicans praised Boehner for his actions, expressing their eagerness to start the new Congress in a position of strength to fully exploit their gains in the midterm elections. But others worried about the potential political fallout from a fresh racial controversy for a party eager to show its broadening appeal to minorities ahead of the 2016 presidential election.

John Weaver, a GOP consultant who advised the presidential campaigns of Sen. John McCain (R-Ariz.), said in an e-mail that Scalise “cannot serve in leadership in our party as we’re in the process of trying to show the American people we can handle the burden of governing, especially in a country so divided across all demographic lines.”

The twin controversies could also derail the carefully laid plans of Boehner and the incoming Senate majority leader, Mitch McConnell (R-Ky.), to shape the party’s message and Washington’s political agenda in the coming weeks. The Republican leaders are poised to make final decisions by Friday about which legislation to hold votes on in the early days of the new Congress. The Senate is expected to focus on bills related to energy policy, while the House is most likely to focus on general economic and job-creating proposals.

From threatening a reporter to tax-evasion charges, here's a look at Rep. Michael Grimm’s 2014 and what led to the New York Republican’s resignation. (Pamela Kirkland/The Washington Post)

Some Republicans also are hoping to focus on immigration and border-security policy, a fight that Democrats have been preparing for since President Obama’s executive action delaying deportation for many immigrants. A controversy involving race could complicate Republican bargaining power.

In a flurry of phone calls late Monday into Tuesday, Scalise reassured his colleagues that he had been oblivious to the racist and anti-Semitic associations of the group when he addressed it in 2002 as a state legislator. In a statement, he called his appearance “a mistake I regret,” emphasizing that it was only to promote his tax-cutting agenda as a Louisiana state representative.

“As a Catholic, these groups hold views that are vehemently opposed to my own personal faith, and I reject that kind of hateful bigotry,” he said. “Those who know me best know I have always been passionate about helping, serving, and fighting for every family that I represent. And I will continue to do so.”

Hoping to quickly put the scandal behind him, Boehner defended Scalise on Tuesday, saying the Louisiana Republican had his “full confidence.” He added that Scalise “made an error in judgment, and he was right to acknowledge it was wrong and inappropriate.” He called Scalise “a man of high integrity and good character.”

Boehner took the opposite approach with Grimm, urging him to step down and then tersely thanking him Tuesday for his service, calling his resignation “the honorable decision.”

“In the last 24 hours, Boehner has twice demonstrated how he is taking charge,” said Karl Rove, an adviser to President George W. Bush. “Both incidents show Boehner is capable of leading with both caution and conviction.”

But Grimm’s resignation could mean a fresh headache for Republicans if Democrats win the seat, which is a possibility in a district where Obama captured 52 percent of the vote in 2012.

It will be up to a Democrat, New York Gov. Andrew M. Cuomo, to decide whether to hold a special election to replace Grimm. Republican Daniel M. Donovan Jr., the district attorney for Richmond County, has been mentioned by New York politicos as a possible candidate. Democrats mentioned include Michael Cusick, a state assemblyman, and former congressman Michael E. McMahon.

Grimm’s announcement that he will resign next Monday ended months of controversy for the lawmaker, a former FBI agent once considered a star GOP recruit. He left the powerful House Financial Services Committee in the spring after federal prosecutors unveiled a 20-count indictment, but he refused to resign and won reelection for a third term in November despite his troubles.

Grimm made up his mind to resign after he spoke with Boehner, who urged him to give up his office, according to associates familiar with their telephone call.

Rep. Jason Chaffetz (R-Utah), the incoming chairman of the House Oversight and Government Reform Committee, was among the dozens of rank-and-file members who defended Scalise.

“I was a chief of staff for a governor, and I saw a state representatives thinly staffed, if at all. They’re young and eager,” he said. “It sounds like something he shouldn’t have done, but if that’s all there is to it, it’s time to move on and tackle bigger, more important things.”

Another Utah Republican, Mia Love, who is one of two black Republicans taking House seats next week, said in a statement that while she had not talked to Scalise about his 2002 appearance, “From my experience, the Majority Whip has been extremely helpful to me and all of my colleagues.”

Scalise and other party leaders have heralded the election of Love and Texas Republican Will Hurd, a black former CIA operative, as a sign of the GOP’s diversifying ranks.

But conservative activists and more mainstream operatives were fretting about the Scalise controversy’s implications for the party’s image.

“It’s always a step forward and two or three steps backward with this kind of stuff. We’ve got to get beyond that,” said Michael Steele, former Maryland lieutenant governor and past chairman of the Republican National Committee.

One of his party’s most prominent black members, Steele suggested that Scalise might have to relinquish his leadership position, just as then-Senate Majority Leader Trent Lott (R-Miss.) did in 2002 after making laudatory comments about Sen. Strom Thurmond (R-S.C.), who was a former segregationist.

“How Do You Show Up at a David Duke Event and Not Know What It Is?” Erick Erickson, a widely followed radio talk-show host and conservative blogger, said in a Twitter message.

Democrats seized on the controversy but stopped short of calling for Scalise’s ouster.

A spokesman for House Minority Leader Nancy Pelosi (D-Calif.) called the incident “deeply troubling” and used it as a way to fault House Republicans for not reauthorizing the Voting Rights Act and for joining lawsuits challenging Obama’s recent executive actions to change immigration policy.

A wider Democratic pile-on appeared to be thwarted in part by Rep. Cedric L. Richmond, the only black Louisiana Democrat in Congress.

“I don’t think Steve Scalise has a racist bone in his body,” Richmond told the New Orleans Times-Picayune. “Steve and I have worked on issues that benefit poor people, black people, white people, Jewish people. I know his character.”

Richmond added that he was not going to let partisan critics “use Steve as a scapegoat to score political points when I know him and know his family.”

Other Republicans said Scalise’s troubles were a media-driven affair.

“This is an absurdity,” former House speaker Newt Gingrich said in an e-mail. “Twelve years ago Scalise made a mistake in judgment while giving speeches on the state budget. Among Democrats there was a dispensation for Justice Hugo Black, who was an active Klan member, and for [former West Virginia senator Robert C.] Byrd, who once led his local Klan group.”

Scalise declined all interview requests and spent Tuesday at his suburban New Orleans home. Aides said he had spoken with Boehner by telephone Monday and was in touch with Majority Leader Kevin McCarthy (R-Calif.), with whom he has a closer relationship.

“We’ll be able to get beyond it,” Rep. Tom Cole (R-Okla.), an ally of the leadership, said of the Scalise situation. “This is going to be an important year for House Republicans. We’ve got the Senate with us now, and we’re going to take on big issues. This whole episode has been a shame for Scalise, but it’s only a distraction.”