South Dakota Gov. Kristi Noem, facing criticism for a story in her new book about killing her dog, suggested that President Biden should do the same with his former dog, Commander. 

In her book, Noem writes about killing her dog, a 14-month-old wirehaired pointer named Cricket after the dog had shown aggressive behavior. Noem also writes that if she got to the White House, she would say "Commander, say hello to Cricket." 

Mr. Biden's dog had been known for biting people at the White House. The German shepherd was removed from the White House last year in the wake of multiple documented reports of aggressive behavior toward Secret Service staff members. 

Noem said on "Face the Nation" on Sunday that the "president should be held accountable" for the dog's actions. When moderator Margaret Brennan asked if she was saying the dog should be shot, Noem answered again "that's what the president should be accountable to." 

"How many people is enough people to be attacked and dangerously hurt before you make a decision on a dog?" the Republican governor said. 

Defending the action, and its inclusion in the book, Noem has said that she was protecting her children, noting that it was a difficult decision. She said in an interview with "CBS Mornings" on Monday that "the purpose of telling the story was so that people would know I don't pass my responsibilities on to anybody else."

But questions have swirled about Noem's political future in recent days. Noem had been considered among a list of possible vice presidential picks to run alongside former President Donald Trump in November's election. But former House Speaker Newt Gingrich said that with the decision, she "ended any possibility of her being picked as VP," although Noem was among potential vice-presidential picks at a Republican donors' retreat at Palm Beach, Florida, over the weekend. 

Kaia Hubbard

Kaia Hubbard is a politics reporter for CBS News Digital based in Washington, D.C.

Twitter