WASHINGTON — President Trump has notified Kim Jong-un, the North Korean leader, that he has canceled their much-anticipated meeting to discuss steps toward denuclearization and peace because of recent “tremendous anger and open hostility” by Pyongyang toward members of his administration.

In a letter dated Thursday to Mr. Kim, the American president left open the possibility that the two could meet in the future. But hours later, Mr. Trump warned that the United States and its allies are prepared to respond should “foolish or reckless acts be taken by North Korea.”

“I feel it is inappropriate, at this time, to have this long-planned meeting,” Mr. Trump wrote in the letter, referring to the summit that had been set for June 12 in Singapore.

But, he added, “You talk about your nuclear capabilities, but ours are so massive and powerful that I pray to God they will never have to be used.”

[Read the text of the letter.]

At a White House bill signing ceremony, Mr. Trump said the United States military is “more ready” than ever to respond to North Korea. He also maintained American sanctions — what he called “by far, the strongest” to be imposed — would continue to exert pressure on North Korea.

Mr. Trump’s reference to anger and hostility followed comments from a North Korean official who described Vice President Mike Pence as “ignorant and stupid.”

Mr. Pence had said that relations with North Korea “will only end like the Libyan model ended if Kim Jong-un doesn’t make a deal.” He made the comments in an interview on Monday with Fox News.

Mr. Pence was referencing the fate of the government of Col. Muammar el-Qaddafi, the former Libyan dictator. Colonel Qaddafi gave up his nuclear program in 2003 in the hope of negotiating with the West, but was killed by rebels in a 2011 uprising after his government was weakened during military action from the United States and its European allies.

When it was noted that the comparison could be interpreted as a threat, Mr. Pence replied, “Well, I think it’s more of a fact.”

In a statement carried by the North’s official Korean Central News Agency, Vice Foreign Minister Choe Son-hui of North Korea said that Mr. Pence had made “unbridled and impudent remarks that North Korea might end like Libya.”

Citing “unlawful and outrageous acts” by top American officials, Ms. Choe said that she would recommend to Mr. Kim that he should reconsider what would have been a historic summit.

The decision to scrap the meeting is the latest turn in the wildly vacillating relationship between Mr. Trump and Mr. Kim. The two have exchanged nuclear threats and also traded derisive nicknames for the other, with Mr. Trump calling the North Korean leader the “little Rocket Man” and Mr. Kim dubbing the American president as a “dotard.”

The announcement appeared to catch South Korea — where millions of people live within immediate range of the North’s nuclear weapons — off guard.

President Moon Jae-in of South Korea called Mr. Trump’s cancellation of the summit meeting “disconcerting and very regrettable.” Mr. Moon has been trying for months to help stage the summit.

“The denuclearization of the Korean Peninsula and building a permanent peace on the peninsula is a task we cannot give up or delay,” Mr. Moon said in a meeting with his National Security Council, according to his office.

He said the current method of communication between North Korea and the United States doesn’t work to resolve the disputes between the two nations. He urged Mr. Trump and Mr. Kim to talk directly.

Mike Pompeo, the secretary of state, told Congress on Thursday that the United States had been moving forward with plans for the meeting. He said the Americans and North Koreans had agreed to assemble teams to work for the summit, but that the North Koreans had not responded to Washington’s questions about doing so over the past few days.

Mr. Trump has hinted over the past week that the summit may or may not take place but has said it would be good for North Korea if it did. “We were informed that the meeting was requested by North Korea, but that to us is totally irrelevant,” Mr. Trump wrote in his letter on Thursday.

“I felt a wonderful dialogue was building up between you and me, and ultimately, it is only that dialogue that matters,” Mr. Trump wrote to Mr. Kim. “Some day, I look very much forward to meeting you.”

In the letter, Mr. Trump thanked Mr. Kim again for the release of three American hostages on May 9, in what was seen as eliminating a big obstacle to the planned peace summit. And the president told the North Korean leader to call or write him if he wants to speak.

Mr. Trump has previously taken partial credit for arranging the meeting, which would have been the first time a sitting American president met face-to-face with the North Korean leader. After the announcement of the date and place of the summit, Mr. Trump appeared to revel in suggestions from others that he win the distinguished Nobel Peace Prize for the feat. The United States had already produced commemorative coins to mark the meeting.

Senator Bill Nelson, Democrat of Florida, blamed the president for the scrapped meeting.

“The cancellation of this summit reveals the lack of preparation on the part of President Trump in dealing with a totalitarian dictator like Kim Jong-un,” Mr. Nelson said in a statement.

Just hours before the White House announced the cancellation, North Korea said it had destroyed its only known nuclear site. CNN’s Will Ripley was in North Korea and read out the Trump letter to North Korean officials.

“I can tell you there was a real sense of shock,” Mr. Ripley said.

“They immediately got up and left.”

Still, North Korean last week threatened to call off the summit if the United States planned to insist on “unilateral nuclear abandonment.”

Mr. Kim said his country would never follow the path of Libya and Iraq. He said those nations met a “miserable fate” at the hands of “big powers.”