President Trump on Thursday sent a letter to the North Korean leader, Kim Jong-un, pulling out of a highly anticipated summit meeting next month and accusing the North Koreans of bad faith. But the next day, he said that his administration was back in touch with North Korea, and that the meeting may be rescheduled.

North Korea had been infuriated over comments from Mr. Trump’s national security adviser, John R. Bolton, describing the voluntary disarmament of Libya in 2003 as a precedent for the negotiations with North Korea. A North Korean official later labeled Vice President Mike Pence a “political dummy” and threatened a “nuclear-to-nuclear showdown” after he echoed Mr. Bolton’s sentiments.

Mr. Trump, however, said he was pleased with a conciliatory statement from North Korea that said the country was willing to give Mr. Trump “time and opportunity” to reconsider his decision.