Wallace's comment came during a radio appearance Friday on The Mike Gallagher Show, in which the two began joking about Gallagher's weight. And then with one comment, Gallagher, 54, brought up Clarkson, 32.
"Listen, don't fat shame me. You do a lot of fat shaming," Gallagher said, according to an audio and transcript by Media Matters. "That's the new phrase now, 'fat shaming.' Have you seen Kelly Clarkson? You know the singer, Kelly Clarkson? Holy cow, did she blow up."
At first Wallace, 67, didn't engage.
"Really? Do we want to talk about some of your friends?" he said. He later added, "Kelly Clarkson's got a lovely voice."
But then he continued, "She could stay off the deep dish pizza for a little while."
Van Susteren, 60, discussed the exchange on her blog Friday. "This 'guy snickering' about her weight is obnoxious. He should apologize," she wrote.
Wallace issued a public apology to Clarkson on Sunday.
He told PEOPLE in a statement "I sincerely apologize to Kelly Clarkson for my offensive comment."
"I admire her remarkable talent and that should have been the focus of any discussion about her," he added.
Clarkson has not commented on the drama, but she has long battled excessive scrutiny over her weight.
The pop singer discussed weight critics with Ellen Degeneres during a Friday appearance on her show.
Clarkson said, "I think what hurts my feelings for people is that I'll have a meet-and-greet after the show and a girl who's like bigger than me will be in the meet-and-greet and be like, 'Wow, if they think you’re big I must be so fat to them.' And it's like, you're just who you are."
Reporting by JENNIFER HEYDE