Speaker John Boehner said Tuesday King's comments were "wrong" and could overwhelm House Republican efforts to overhaul immigration laws, Politico reported.
"There can be honest disagreements about policy without using hateful language," Boehner said in a statement Tuesday. "Everyone needs to remember that."
House Majority Leader Eric Cantor, the No. 2 House Republican, said he "strongly" disagreed with King's "characterization of the children of immigrants and finds the comments inexcusable."
Cantor is working on a bill that would legalize young undocumented immigrants.
King said in an interview last week with Newsmax a large number of immigrants brought into the United States illegally as children were smuggling drugs into the country.
"Some of them are valedictorians, and their parents brought them in," King said. "It wasn't their fault. It's true in some cases, but they aren't all valedictorians. They weren't all brought in by their parents."
"For everyone who's a valedictorian, there's another 100 out there that weigh 130 pounds and they've got calves the size of cantaloupes because they're hauling 75 pounds of marijuana across the desert," King said. "Those people would be legalized with the same act."
During in a hearing Tuesday by a House panel specifically convened to examine legalization for young undocumented immigrants, Rep. Joe Garcia, D-Fla., criticized King's remarks as "inflammatory" and "offensive."
"When members of this committee -- when members of this House -- use inflammatory language, use offensive language, it does not help the progress," Garcia said.
When King spoke, he declined to address his comments or respond to Garcia's remarks, Roll Call said.
In an interview with Radio Iowa, he said he got the physical description from law enforcement, Roll Call said.
"It's not something that I'm making up. This is real," King said during the radio interview. "We have people that are mules, that are drug mules, that are hauling drugs across the border and you can tell by their physical characteristics what they've been doing for months, going through the desert with 75 pounds of drugs on their back.
"[If] those who advocate for the DREAM Act, if they choose to characterize this about valedictorians, I gave them a different image that we need to be thinking about because we just simply can't be passing legislation looking only at one component of what would be millions of people."