President Trump has agreed to meet with North Korean leader Kim Jong-un by May for historic talks on denuclearization, a senior South Korean official announced Thursday night.

South Korean National Security Adviser Chung Eui-yong told reporters at the White House that Mr. Kim conveyed the invitation for a meeting with Mr. Trump after breakthrough talks this week between the North and South in Pyongyang.

Mr. Trump called the development “great progress” but vowed that the U.S. would not lift sanctions on North Korea while diplomacy is under way.

Mr. Chung said the North Korean leader “expressed his eagerness to meet President Trump as soon as possible.”

South Korean President Moon Jae-in already had been scheduled to meet with the North Korean leader at a summit in April at the Demilitarized Zone between the two Koreas. Mr. Chung is part of a South Korean delegation visiting Washington following the talks this week in Pyongyang.

Mr. Chung said the North Korean leader is “committed to denuclearization” and that he pledged to refrain from any further nuclear weapons or ballistic missile tests. He said Mr. Kim also has accepted that the U.S. and South Korea will proceed with “routine” military exercises scheduled for next month.

“I explained to President Trump that his leadership and his maximum pressure policy, together with international solidarity, brought us to this juncture,” Mr. Chung said, adding that he expressed Mr. Moon’s “personal gratitude” for Mr. Trump’s leadership on confronting Pyongyang.

Mr. Trump tweeted Thursday night about the sudden announcement: “Kim Jong Un talked about denuclearization with the South Korean Representatives, not just a freeze. Also, no missile testing by North Korea during this period of time. Great progress being made but sanctions will remain until an agreement is reached. Meeting being planned!”

There has never been a face-to-face meeting between the leaders of the U.S. and North Korea. A senior administration official said Mr. Kim conveyed the message by word of mouth through the South Koreans that he wants to meet with Mr. Trump “as quickly as possible.”

The South Korean officials briefed Mr. Trump in the Oval Office on Thursday, with National Security Adviser H.R. McMaster, Defense Secretary James Mattis, White House Chief of Staff John F. Kelly and other U.S. officials present.

The official said Mr. Trump agreed to meet with Mr. Kim “in a matter of a couple of months.”

While the U.S. has often made concessions to North Korea in return for lower-level talks, the official said that keeping sanctions in place “is what differentiates the president’s policy from the policies of the past.”

“President Trump has been very clear from the beginning that he is not prepared to reward North Korea in exchange for talks,” the aide said.

White House press secretary Sarah Huckabee Sanders confirmed that Mr. Trump will meet with Mr. Kim “at a place and time to be determined.”

“We look forward to the denuclearization of North Korea. In the meantime, all sanctions and maximum pressure must remain,” she said.

Mrs. Sanders said the president “greatly appreciates the nice words of the South Korean delegation and President Moon.”

Mr. McMaster is to brief U.N. Security Council envoys on North Korea on Monday, Reuters reported.

As the prospect of direct Trump-Kim talks has risen, analysts and U.S. intelligence officials have noted that the North Korean dictator, in his mid-30s, has had hardly any interactions with high-profile Americans. The exception is multiple meetings in recent years with former basketball star Dennis Rodman.

It’s a factor that has made it hard for U.S. intelligence to predict how Mr. Kim might behave in a meeting with Mr. Trump and created a challenge for officials tasked with briefing the president on what to expect.

Some analysts warned Thursday night that the risks remain incredibly high that hopes for diplomacy could fizzle on both the U.S. and North Korean side.

“We’d expect such an unprecedented meeting to happen after some concrete deliverables were in hand, not before,” said Suzanne DiMaggio, a senior fellow with the New America think tank in Washington.

While Ms. DiMaggio said that if the developments evolve into “a process for serious, sustained negotiations,” then Mr. Trump’s willingness to embrace North Korea’s reported offer will turn out to be a “positive move.”

“But it will have to be managed very carefully with a great deal of preparatory work,” she told The Times on Thursday night. “Otherwise, it runs the risk of being more spectacle than substance. Right now, Kim Jong-un is setting the agenda and the pace, and the Trump administration is reacting.”

“The administration needs to move quickly to change this dynamic,” Ms. DiMaggio said.

Analysts have also warned that there has yet to be an official offer for talks directly from the Kim regime — that all of the latest news developments on the situation have come through the South Korean government.

As of early Friday, Korean time, the North’s official Korean Central News Agency had not mentioned the events in Washington.

“There seems to be no direct message from North Korea to the U.S. government,” Michael Pillsbury, a Mandarin-speaking Pentagon consultant and head of Chinese strategy at the Hudson Institute in Washington, noted on Wednesday.

“This is all being filtered through the South Korean government,” said Mr. Pillsbury, adding that Chinese officials, who are generally regarded to be far more in touch than anyone else with goings-on in Pyongyang, have also been unsure about the South Korean claims of Mr. Kim’s eagerness to talk with Mr. Trump.

The Chinese government has yet to make an official statement on the situation, and the de facto newspaper of the ruling Communist Party in Beijing went so far as to question whether Mr. Kim’s offer to Mr. Trump really happened.

“North Korea still has not confirmed the South’s version of events,” stated an editorial in the Global Times, which also pointed out that Pyongyang’s official state newspaper, the Rodong Sinmun, had asserted in its editorial that the Kim regime plans to proceed with the “advance” of the nation’s “nuclear weaponry.”

Earlier Thursday, Secretary of State Rex W. Tillerson played down hopes for a breakthrough on North Korea’s nuclear program, saying the U.S. is a long way from negotiations after the country’s leader offered to give up his weapons in exchange for security guarantees.

“We’re a long way from negotiations; we just need to be very clear-eyed and realistic about it,” Mr. Tillerson said during a stop in Addis Ababa, Ethiopia.

Mr. Moon’s office said Tuesday that the North had expressed a “willingness to hold a heartfelt dialogue with the United States on the issues of denuclearization” and “made it clear that while dialogue is continuing, it will not attempt any strategic provocations, such as nuclear and ballistic missile tests.”

China barely reacted to word of a possible thawing of relations.

U.S. officials believe that sanctions against North Korea are beginning to sting the communist country, which has staged multiple nuclear and ballistic missile tests in violation of U.N. Security Council resolutions.

Administration officials also have repeatedly pointed out that Mr. Kim has gone through the motions of talks with the U.S. previously, all the while continuing to refine his weapons programs.

Rep. Edward R. Royce, California Republican and House Foreign Affairs Committee chairman, said Mr. Kim’s desire for talks “shows sanctions the administration has implemented are starting to work.”

“We can pursue more diplomacy as we keep applying pressure ounce by ounce,” Mr. Royce said. “Remember, North Korean regimes have repeatedly used talks and empty promises to extract concessions and buy time. North Korea uses this to advance its nuclear and missile programs. We’ve got to break this cycle.”

Part of what made the announcement so unexpected is that from the start of his presidency, Mr. Trump has determined to take a more aggressive approach to North Korea than his predecessors.

He has taunted Mr. Kim on Twitter as “Little Rocket Man” and vowed last year that Pyongyang would be met with “fire and fury” if Mr. Kim followed through on threats to attack the U.S. mainland or its territories. Mr. Trump also has pressed China to adhere to harsh economic sanctions.

That history prompted one key Democrat to warn the U.S. president about diplomacy by Twitter.

Mr. Trump needs to “abandon his penchant for unscripted remarks and bombastic rhetoric to avoid derailing this significant opportunity for progress,” said Sen. Edward J. Markey of Massachusetts, the top Democrat on the East Asia panel of the Senate Foreign Relations Committee.

“And if the talks between the two leaders do not go well, it is not an excuse to justify military action for a situation that has no military solution,” Mr. Markey said.

Retired Rear Adm. John Kirby, who was a spokesman for the Pentagon and State Department in the Obama administration, said on CNN. “It certainly does feel like a different moment.”

He said Mr. Trump deserves credit for the announcement, though he also cited Seoul, saying Mr. Moon may be the most eager South Korean leader ever to produce a breakthrough with the North.

Kevin Martin, president of Peace Action, said Mr. Kim’s reported commitment not to test nuclear weapons or ballistic missiles during diplomacy “is excellent news, as is President Trump accepting Kim’s invitation to meet in person for the first time.”

“North Korea is putting virtually all topics of concerns on the table,” Mr. Martin said. “Trump now has the opportunity to achieve what no president has been able to achieve in seven decades of U.S.-North Korea relations: make real strides towards lasting peace on the Korean Peninsula.”

• Guy Taylor contributed to this article.

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