One, a top member of the Congressional Black Caucus on Monday said he will file a motion to censure King.
Rep. Bobby Rush, Democrat of Illinois, said Congress "cannot be a platform for Steve King and those of his ilk," according to The Hill.
"He has become too comfortable with proudly insulting, disrespecting, and denigrating people of color. As with any animal that is rabid, Steve King should be set aside and isolated," Congressman Rush said in a statement.
"His rabid racism continues to stain and embarrass this body and the years of deliberate silence from Republicans have only emboldened his ignorant and immoral behavior and empowered those who emulate him," Rush charged.
Rep. King, who has been sent to Congress nine times by his Iowa constituents, asked The New York Times in an interview last week when "white nationalist" and "white supremacist" became "offensive."
Separately, Rep. Tim Ryan (D-OH) introduced a resolution to censure King, charging that King's comments "legitimize White supremacy and White nationalism as acceptable in today's society," and "are abhorrent to the founding principles of our nation and our rich history of diversity and tolerance of those who backgrounds and beliefs have made America the envy of the world," The Hill added.
Congressman King late last week took to the floor of the House to say that he denounced the "evil ideologies" of white nationalism and white supremacism, but his past remarks and actions over many years make clear he supports them. He later chalked up making the racist remarks as a "rookie mistake."
Also separately, House Majority Whip James Clyburn (D-SC) said he would introduce a resolution to rebuke, but not censure Rep. King.
Meanwhile, some Republicans in the House and Senate have condemned King's remarks, but not his actions or positions.
This is the first test for House Minority Leader Kevin McCarthy (R-CA), who says he will take action.
"I'm having a serious conversation with Congressman Steve King about his future and role in this Republican Party," McCarthy told "Face the Nation."
"I will not stand back as a leader of this party, believing in this nation that all are created equal, that that stands or continues to stand and have any role with us."
King, a nine-term Congressman who represents a district that is more than 95 percent white, is perhaps best-known for accusing undocumented immigrants of having "calves the size of cantaloupes" from "running drugs across the Mexican border."
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