White House press secretary Sarah Huckabee Sanders praised a move by House Republicans to strip the nine-term Iowa lawmaker of his committee assignments.
King told The New York Times last week that, "White nationalist, white supremacist, Western civilization - how did that language become offensive?"
The comments were widely denounced as racist.
The House on Tuesday approved a Democratic measure rebuking King, and a member of the House Republican leadership suggested King should leave Congress.
When President Donald Trump was asked on Monday about King's remarks, he said: "I haven't been following it." But Sanders said Wednesday that King's comments were "abhorrent," and said GOP leaders took action when one of their members said "outrageous and inappropriate things."
House Democratic leaders, meanwhile, blocked an effort to censure King, referring a proposal by Illinois Rep. Bobby Rush to the House Ethics Committee for further review.
Censure is the most serious sanction for a House member short of expulsion, and it has been imposed only six times in the past 100 years.
Rush, the sole House member to oppose the earlier measure rebuking King, pressed for a vote Wednesday to censure King, saying the House should take a stronger stand against what he called "Steve King's violent, vitriolic and rabid racism."
After the House clerk read Rush's resolution detailing a string of inflammatory comments by King over the years, House Majority Leader Steny Hoyer of Maryland moved to refer the matter to the Ethics Committee. Lawmakers approved the motion on a voice vote, postponing action on the censure measure indefinitely.
"I think we have spoken, and we have spoken on both sides of the aisle, that this is unacceptable rhetoric and behavior," Hoyer said.
House Majority Whip James Clyburn, D-S.C., who sponsored the disapproval motion, said censure should be reserved for statements made on the House floor. He and other Democratic leaders also said censuring King could open Democrats to Republican attacks.
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