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The speaker of the Republican-dominated House of Representatives, Paul Ryan, and the leading Democrat in the chamber, Nancy Pelosi, both took exception to King's remarks.
The Iowa congressman on Sunday posted a tweet praising Geert Wilders, a nationalist, anti-Islam politician vying to become the Netherlands' prime minister in a national election on Wednesday.
"Wilders understands that culture and demographics are our destiny. We can't restore our civilization with somebody else's babies," King wrote in a post that drew thousands of "likes."
Pelosi on Monday called on House Republican leaders to condemn King's comments, saying they "must decide whether white supremacy is welcome in the GOP ranks."
A spokeswoman for Ryan, AshLee Strong, said, "The speaker clearly disagrees (with King) and believes America’s long history of inclusiveness is one of its great strengths."
King, an early supporter of Donald Trump in last year's presidential election, defended his tweet in an interview on CNN on Monday. He pointed to Western Europe, where he said low birth rates were harming civilization, culture and values.
"I'd like to see an America that is just so homogenous that we look a lot the same," he said. "I think there's far too much focus on race, especially in the last eight years. I want to see that put behind us."
Pressed on birth rates for different groups of Americans, King said: "They contribute differently to our culture and civilization."
Some of King's House colleagues appeared to take his tweet personally.
"What exactly do you mean?," tweeted Republican U.S. Representative Carlos Curbelo of Florida. "Do I qualify as 'somebody else's baby?' #concernedGOPcolleague."
Democratic Representative Ted Lieu, who immigrated to the United States at age 3, tweeted a picture of his two sons, writing: "Dear Representative Steve King: These are my two babies -- Representative Ted Lieu."
Former Florida Governor Jeb Bush said, "America is a nation of immigrants," and added that King's sentiment "doesn't reflect our shared history or values." Bush was one of Trump's Republican rivals for the White House.
The tweet also drew fire from the NAACP Legal Defense and Educational Fund. The head of the civil and human rights law firm, Sherilyn Ifill, said King's remarks were "an explicit call to return to the shameful period when white supremacy was the norm in American public life."
Ifill said King's remarks were "particularly dangerous" at a time when violent hate crimes have reached "dangerous levels."
King is from a rural state where nearly 92 percent of the population is white, compared with 77 percent for the nation as a whole, according to the U.S. Census Bureau.
Jeff Kaufmann, head of the Republican Party in Iowa, said in a statement that he disagreed with King, also calling the United States "a nation of immigrants" and saying that such diversity was its strength.