“I saw the remark that she made,” Mr. Pompeo said of Ms. Choe. “We are hopeful that we can continue to have conversations and negotiations.”

Mr. Pompeo added that Mr. Kim had made multiple promises during the Hanoi summit meeting to Mr. Trump that he would take steps to wind down his nuclear program. Despite the unpredictable messaging, he said, the administration would continue to take Mr. Kim at his word.

Mr. Bolton, for his part, told reporters at the White House that any suggestion that he and Mr. Pompeo undermined the negotiations were inaccurate, and that he had been in touch with national security officials in South Korea about the remarks.

“We’ve discussed their reaction and our reaction,” Mr. Bolton said. “I’d like to speak further within the U.S. government before we respond.”

The office of South Korea’s president, Moon Jae-in, who did much to broker the talks between the North and the United States, said it was closely monitoring the situation. “Whatever the situation, our government will try its best to help resume North Korea-U.S. negotiations,” it said in a statement.

The breakdown of the Hanoi meeting revealed a wide gap between North Korea and the United States over how to proceed with denuclearization.

North Korea insisted, as it has before, on moving in phases. In Hanoi, Mr. Kim offered to dismantle the plutonium, uranium-enrichment and other facilities at its Yongbyon site, north of Pyongyang, and demanded that Washington in return lift crucial sanctions that have been imposed on the North since 2016.