President Trump has praised Governor Noem of South Dakota, often mentioned as a top candidate to be his running mate in 2024, saying he likes her “a lot.”

“She had a rough couple of days. I will say that,” Mr. Trump said in an interview with Wisconsin’s Spectrum News 1 on Tuesday. Asked about the list of names he’s considering for the veep slot, he said: “I like her a lot,” adding, “I don’t want to comment on anybody on the list.”

Mr. Trump spoke after Ms. Noem had been roundly ripped for several anecdotes in her new book, “No Going Back,” which hit the stands on Tuesday. In it, she says she killed a young dog on her farm that she deemed “untrainable,” and claimed to have met with the North Korean dictator, Kim Jong-un, which reporters quickly proved never happened.

Ms. Noem recently attended an event at Mar-a-Lago, where hundreds of GOP donors and supporters convened for a spring retreat organized by the Republican National Committee. The gathering was notable for featuring appearances from several individuals widely considered as potential candidates for the vice presidency in future elections, including Senator Scott of South Carolina and Senators Rubio and Vance.

The fallout over her book has prompted Ms. Noem to shift her schedule, with two high-profile interviews being canceled at the last minute. Both Fox News’s Greg Gutfeld and CNN’s Dana Bash announced the cancellations, though reasons for the changes in plans were not immediately disclosed.

“Governor Noem was scheduled to be on this program, ‘Inside Politics,’ today,” Ms. Bash said on Wednesday. “Her team reached out to us weeks ago to book her here and we reconfirmed this week. She abruptly canceled last night. We want to say that, governor, you are of course welcome on the program anytime.”