"That language has no place in America", McCarthy said.
King said in an interview last week, "White nationalist, white supremacist, Western civilization-how did that language become offensive?"
"I will admit I am unsure who is offended by the term "Western civilization" on its own, but anyone who needs "white nationalist" or "white supremacist" defined, described and defended does lack some pretty common knowledge", Scott wrote in the The Washington Post.
For years, King appeared untouchable by Republican leaders.
Shortly before the 2018 midterm elections, in which King was running, Representative Steve Stivers of OH, then the head of the GOP campaign committee, issued an extraordinary public denunciation of him.More news: Paul Manafort Allegedly Shared 2016 Polling With Russia-Linked Associate
More news: First Flu Death in Kane, 3-Year-Old Girl
More news: Hotstar removes KWK's Hardik Pandya-KL Rahul episode after the huge controversy
King also released a statement on Monday night that claimed he only meant to defend "Western civilization" - not white supremacy.
A prominent Republican lawmaker, King faces losing his chairmanship of the House Judiciary subcommittee on Constitution and Civil Justice as well as his membership in the Agriculture, Small Business and Judiciary committee.
"I think he ought to step aside and I think Congress ought to make it very clear he has no place there", the 2012 Republican presidential nominee said on Capitol Hill. And I will tell you this: I've watched on the other side that they do not take action when their members say something like this.
But the Republican leadership has been closely following the story.
King met Monday afternoon with McCarthy of California. President Donald Trump was roundly criticized - including by Scott and other Republicans - for his failure to condemn white supremacists following a violent 2017 rally in Charlottesville, Virginia, that left one counter-protester dead.
"Some in our party wonder why Republicans are constantly accused of racism - it is because of our silence when things like this are said". King has made at least six trips to Austria while in Congress and gave an interview to a far-right newspaper there where he decried the country's "Nazi guilt".
"So today I denounce the words of Rep. Steve King and I do so invoking the words of another king, Dr. Martin Luther King Jr, who if would have been allowed to live, would be celebrating his 90th birthday tomorrow", Clyburn said on the House floor. Steve King said in a New York Times article published Thursday. State Sen. Randy Feenstra, R-Hull, announced this week he'd seek the Republican nomination, facing the nine-term King.