The White House condemned as “disturbing” and “absurd” comments in which Kristi Noem, the Republican governor of South Dakota and a potential running mate for Donald Trump, threatened to harm or kill Joe Biden’s dog.

“We find her comments from yesterday disturbing,” Karine Jean-Pierre, Biden’s press secretary, told a White House briefing. “We find them absurd. This is a country that loves dogs, and you have a leader that talks about putting dogs down, killing them.”

Noem’s bizarre threat is contained in No Going Back, a campaign book that generated unusual buzz after the Guardian revealed how Noem describes in detail the day she shot dead her dog Cricket, which she deemed untrainable and dangerous, and an unnamed goat.

The revelation sparked a political firestorm, widely held to have incinerated Noem’s chances of being named running mate to Trump, the presumptive Republican presidential nominee.

But as the book neared publication on Tuesday, it became clear Noem was not done when she closed her chapter on killing Cricket, a 14-month-old female wirehaired pointer, and the unnamed male goat, which Noem says was smelly and aggressive and dangerous to her children.

At the end of No Going Back, Noem asks: “What would I do if I was president on the first day in office in 2025?”

She continues: “The first thing I’d do is make sure Joe Biden’s dog was nowhere on the grounds. (‘Commander, say hello to Cricket for me.’)”

Noem adds that her dog Foster “would sure be welcome” at the White House.

“He comes with me to the [state] capitol all the time and loves everyone,” she writes.

Regardless, a governor widely held to have designs on the presidency in 2028 has at least implied, in print, that she would have a predecessor’s dog killed.

Noem has defended her description of killing Cricket and the goat as evidence of her willingness to do unpleasant but necessary things in farm life as well as in politics.

Commander, a German shepherd owned by Joe and Jill Biden, was removed from the White House after biting Secret Service agents.

On Monday, Jean-Pierre said: “Commander’s living with family members.”

The day before, Noem had defended her comments.

Her host on CBS’s Face the Nation, Margaret Brennan, quoted Noem’s apparent threat to kill Commander and asked: “Are you doing this to try to look tough? Do you still think that you have a shot at being a VP?”

Noem said: “Well, number one, Joe Biden’s dog has attacked 24 Secret Service people. So, how many people is enough people to be attacked and dangerously hurt before you make a decision on a dog and what to do with it?”

Brennan said: “Well, he’s not living at the White House any more.”

Noem said: “That’s a question that the president should be held accountable to.”

Brennan said: “You’re saying he [Commander] should be shot?”

Noem said: “That what’s the president should be accountable to.”

Noem tried to move on, to talk about Covid in South Dakota. But she also said she was “so proud” of a book that contained “a lot of truthful stories”.

Elsewhere, though, Noem’s publisher, Center Street, said that at Noem’s request it was removing from her book “a passage regarding Kim Jong-un … upon a reprint of the print edition and as soon as technically possible on the audio and ebook editions”.

In her book, Noem writes: “I remember when I met with North Korean dictator Kim Jong-un. I’m sure he underestimated me, having no clue about my experience staring down little tyrants (I’d been a children’s pastor, after all).”

As first reported by the Dakota Scout, no such meeting occurred.

Noem told CBS: “What bothers me the most about politicians is when they’re fake.”

Brennan said: “But if you have to retract … parts of [the book] …”

Noem, whose publisher said it would retract part of her book, said: “I’m not retracting anything.”

Brennan said: “OK.”

On Saturday, Noem attended a Trump Florida fundraiser featuring a host of vice-presidential contenders.

Noem was “somebody I love”, NBC reported Trump as saying, adding: “She’s been with me, and a supporter, and I’ve been a supporter of hers for a long time.”

But unlike other hopefuls, among them the South Carolina senator Tim Scott and the New York congresswoman Elise Stefanik, Noem was not called to the stage.

She reportedly left early.