"Somebody that I love," Trump said of Noem. "She's been with me, a supporter of mine and I've been a supporter of hers for a long time."

Noem had long been viewed as a potential Trump running mate before her disclosure in a forthcoming autobiography about her decision decades ago to kill her family's dog. Since then, the South Dakota Republican's political stock has cratered. Noem has refused to back down from her description of the incident, even arguing that President Joe Biden should treat his dog Commander, who has had many biting incidents, similarly.

Some Republicans have described Noem as toast amid the uproar.

Decades ago, Noem wrote that she killed Cricket after she decided that the dog was untrainable and overly aggressive.

Noem on Sunday tried to defend her memoir, including its inaccurate claim that she met with North Korean leader Kim Jong Un during a combative interview on CBS' "Face the Nation." She also reiterated that killing Cricket illustrates that she won't avoid hard choices.

"The reason that this story is in the book because people need to understand who I am and some of those difficult decisions," Noem told host Margaret Brennan.