In a tweet late Wednesday afternoon, Cheney called King's comments "appalling and bizarre."
"As I've said before, it's time for him to go," said Cheney, who is chairwoman of the House Republican Conference. "The people of Iowa's 4th congressional district deserve better."
In January, Cheney had called for King to "find another line of work" after The New York Times published an interview in which the lawmaker questioned how the terms "white nationalism" and "white supremacy" had become offensive.
King's latest comment drew rebukes from both sides of the aisle. J.D. Scholten, a Democrat who ran against King last year and is challenging him in 2020, said King's remarks are "disrespectful to survivors and don't reflect Iowan values."
"Yet again, Steve King puts his selfish, hateful ideology above the needs of the people of Iowa's 4th district," Scholten said in a statement. "Excusing violence - in any way - is entirely unacceptable."
Republican Randy Feenstra, an Iowa state senator who is waging a primary challenge against King, also condemned the lawmaker's comments.
"I am 100% pro-life but Steve King's bizarre comments and behavior diminish our message & damage our cause," Feenstra said in a tweet. "Trump needs defenders in Congress, not distractions. I will ensure we win this seat & I'll be an effective conservative leader in Congress."
Others denouncing King's remarks on Wednesday included Sen. Kirsten Gillibrand, D-N.Y., a Democratic presidential primary contender who called on King to resign, and Ilyse Hogue, president of the abortion rights group NARAL.
"Steve King - demonstrating there is NO bottom -- defends his position that there should be no exceptions on abortion bans by suggesting that but for rape and incest, there would be no people left," Hogue said on Twitter. "I'm really glad I do not live in his world."
South Bend, Indiana, Mayor Pete Buttigieg, a Democratic presidential candidate, criticized King's remarks during a campaign stop in Tipton, Iowa.
"You would think it would be pretty easy to come out against rape and incest," Buttigieg told reporters. "Then again, you'd think it'd be pretty easy to come out against white nationalism. So this is just one more example why there needs to be a sane representative in that district, and that's why I think J.D. Scholten will be an excellent public servant for people of that district."
King kicked off his bid for a 10th term in Congress in February by declining to apologize for repeatedly making offensive remarks. The previous month, House Republican leaders stripped King of his committee assignments after his comments to The Times. After the censure, King compared himself to Jesus.
Over the years, King has claimed that "our civilization" can't be restored with "somebody else's babies," supported a Toronto mayoral candidate considered to be a white nationalist and met with a far-right Austrian group with historical Nazi ties. He has made a variety of remarks widely viewed as racist, anti-Semitic or insulting to minorities.
