WASHINGTON — Long before Donald J. Trump took aim at immigrants, there was Representative Steve King of Iowa.

Since Mr. King’s election to the House in 2002, and before that in the State Legislature, where he first tried out his English-only trademark talking point, Mr. King, a Republican, has injected himself into the immigration debate with inflammatory and at times boorish statements.

Against the backdrop of an emboldened white nationalist movement in the United States, his Twitter post over the weekend — “We can’t restore our civilization with somebody else’s babies” — suggested that Mr. King was sliding from his typical messages to something far darker. It was praised by both the white supremacist David Duke and The Daily Stormer, a neo-Nazi website.

But it was also quickly criticized by many Republicans, including Speaker Paul D. Ryan, whose office said he “clearly disagrees” with Mr. King, and Representative Carlos Curbelo, Republican of Florida, who is of Cuban descent. Mr. Curbelo responded on Twitter: “What exactly do you mean? Do I qualify as ‘somebody else’s baby?’”