(CNN) Rep. Steve King, the Iowa Republican who has a history of making racially inflammatory remarks, said Friday he was not concerned he would face any backlash from his party after making sympathetic comments towards white supremacists.

Asked if he was worried that GOP leaders would strip him from committee assignments, King told CNN, "I've heard nothing like that -- why would anybody do that?" He also said he has no concerns that the National Republican Congressional Committee won't endorse him in his primary, saying, "They never have -- that's nothing new."

And the Iowa Republican said he's not worried that his comments -- when he told The New York Times, "White nationalist, white supremacist, Western civilization — how did that language become offensive?" -- will affect his chances at re-election. He said he has not heard push back from local Republican leaders in Iowa.

"No one has contacted me with concerns, these folks know me," he told reporters.

King may not be too far off-base. While a senior GOP aide said that King's remarks amounted to a "tipping point," it was hardly clear what next steps GOP leadership would take. On Friday, a top House Democratic leader endorsed an idea about formally censuring King, but it was far from clear whether any Republicans would get behind it as well.

The three top Republicans -- House Minority Leader Kevin McCarthy, House Minority Whip Steve Scalise and GOP Conference Chair Liz Cheney -- all sharply rebuked King over his comments in separate written statements on Thursday.

On Friday, Scalise would not say if King should be punished.

"I think it's important that we all reject that kind of hateful ideology," Scalise told CNN. "It's evil and we ought to reject everything it represents."

Asked if he would support King in his 2020 primary bid, Scalise said, "I haven't even been focusing on the politics of what's going to happen later next year. I mean obviously we're going to have a lot of time for politics."

The comments come at an awkward time for the GOP, which has struggled to attract minorities under President Donald Trump, who has often stoked racial tensions to advance his arguments during his two years in office. Sen. Tim Scott, the lone black GOP senator, wrote in an opinion piece Friday that the GOP should not be silent over King.

"Some in our party wonder why Republicans are constantly accused of racism — it is because of our silence when things like this are said," Scott wrote in The Washington Post.

Other Republicans weigh in

For the most part, however, Republicans have been quiet.

"I don't know," said Rep. Tom Cole, Republican of Oklahoma, when asked if King should be punished. "I think leadership has pushed back, and I know he's put out a clarifying statement."

Asked if he would favor punishing King, Cole said, "I'm not going to get into a public discussion on that."

Indeed, while some Republicans repudiated his remarks, saying they sharply condemn white supremacists, influential GOP lawmakers were uncertain what to do about King.

The most senior Republican in the Senate, Chuck Grassley of Iowa, said this about King's remarks Friday: "I think that any claim of white supremacy is wrong and I detest it."

But Grassley was non-committal about whether he'd back his fellow Iowa Republican again for re-election.

"Very seldom do I get involved in primaries and right now you're two years away from elections," Grassley told CNN. "Ask me maybe in a year and a half or something."

Asked if King was fit to serve in office, Grassley said, "The people of Iowa elected him and so, you know, the people have made a choice."

On the House side, GOP leaders continued to struggle with how to address their controversial member.

Rep. Tom Emmer of Minnesota, who chairs the National Republican Congressional Committee, said Friday he disagrees "vehemently with the comments" and they were "not helpful to what we're trying to do" when asked if King should be punished by the GOP.

"We don't usually get involved in primaries," Emmer told CNN when asked if the party committee would endorse him. Asked if that meant the NRCC also would not support him in a general election should he win the nomination for a 10th term in 2020, Emmer said, "I think it's way too early. ... You're talking two years from now. I mean we don't typically get involved in primaries and that's about all I have to say."

King speaks from the floor

Recognizing the growing controversy, King took to the floor Friday to try to clean it up.

King said he approached Scalise to let him know he planned to discuss the matter on the floor. "I said this is what I'm prepared to do, and we agreed that was a good thing to do." But he made clear no one in the GOP told him to make those remarks.

On the floor, King contended his comments were taken out of context, saying he rejects white supremacist ideology and labels on individuals.

"I regret the heartburn that has poured forth upon this Congress and this country and especially in my state and in my congressional district," King said on the floor. "But the people who do know me know I wouldn't even have to make this statement because they know my life they know my history, they know that I have lived in the same place since 1978."

"I reject that history; I reject that ideology," King said. "I defend American civilization, which is an essential component of western civilization."

As he left the floor, King was asked by reporters if he was worried about losing a ranking member position on a House Judiciary subcommittee. "I've had no discussion about that. I haven't given it any thought," King said. "But the more you guys write about that stuff, then it becomes an issue."

Black Democratic leader backs effort to censure King

While Republicans remained mostly silent, some Democrats weighed their next steps.

Democratic Rep. Tim Ryan of Ohio is considering offering a formal resolution censuring King for the latest in a history of racially tinged remarks. The most senior black leader in Congress, House Majority Whip James Clyburn of South Carolina, told CNN he supports that move.

"You'd have to ask him about that," Clyburn said when asked if he views King as a racist. "I do think he has racial tendencies."

House Speaker Nancy Pelosi told CNN Friday she had yet to see King's remarks when asked if she would back a censure resolution. "I have not seen what he said, but he makes terrible comments all the time, so this is not anything new."

But the head of the Congressional Black Caucus, Rep. Karen Bass, said Friday that Democrats should let Republicans punish King and avoid taking up the matter because, she said, it would easily be dismissed as a partisan issue.

"I'm not sure if censure is the right thing to do, but something absolutely should be done because he has been consistent in his disrespect, disregard for his colleagues," Bass said. "His party needs to absolutely do something definitive. I'm not so sure it should be the House, because if it's the House, then they'll blame it on the Democrats."

Bass added, "He's got a long history of this."

This story has been updated with additional developments Friday.