North Korea, which has been saying its nuclear weapons are nonnegotiable, did not immediately provide its own version of what Mr. Kim had offered. That initial silence fed cautions that he was raising premature optimism, or perhaps strategizing to buy time.
But it seemed unlikely that the South Korean delegation would have publicized such an offer without the North’s assurances, after what by all accounts was an extraordinarily cordial visit. Even President Trump, who has mocked Mr. Kim and vowed “fire and fury” that would obliterate North Korea if its nuclear forces ever attacked, offered a guarded but positive response.
“For the first time in many years, a serious effort is being made by all parties concerned,” Mr. Trump said on Twitter. “The World is watching and waiting! May be false hope, but the U.S. is ready to go hard in either direction!”
Later in Washington, Mr. Trump told reporters: “The statements coming out of South Korea and North Korea have been very positive. That would be a great thing for the world.”
White House officials were more cautious, with one senior official noting that the United States has negotiated with North Korea over its nuclear program off-and-on for 27 years, and that the North Koreans have broken every agreement they ever made with the Americans.
The United States, this official said, has no current plans to further delay joint military exercises with South Korea, suspended for the Winter Olympics last month in Pyeongchang, South Korea. Those exercises are scheduled to resume in April, after the Paralympic Games in Pyeongchang.
While the Trump administration is intrigued by North Korea’s offer — as relayed through the South Koreans — the senior official noted that North Korea could still manufacture missiles and bombs during a pause in testing.
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Two top advisers to President Moon who met with Mr. Kim will visit the White House later this week to give a more detailed briefing on their talks. But the senior official said the United States had confidence in the preliminary assessment they had provided.
That assessment signals the first time Mr. Kim has indicated a willingness to discuss abandoning nuclear arms in return for security guarantees from the United States, which has technically been in a state of war with North Korea for nearly seven decades.
The South Korean delegation gave no indication that North Korea would start dismantling nuclear or missile programs anytime soon. Nonetheless, the delegation’s visit represented major progress in Mr. Moon’s efforts to improve relations with North Korea. Those efforts advanced considerably during the Winter Olympics, to which Mr. Kim sent athletes, entertainers and political delegations that included his sister.
A senior member of the South Korean delegation that returned on Tuesday, Mr. Moon’s national security adviser, Chung Eui-yong, said Mr. Kim had been unexpectedly flexible.
Mr. Chung told reporters in Seoul, the South Korean capital, that the delegation had anticipated Mr. Kim would insist that the South and the United States not hold their military exercises. The South Koreans were wrong.
“Kim Jong-un simply said he could understand why the joint exercises must resume in April on the same scale as before,” Mr. Chung said. “But he said he expected them to be readjusted if the situation on the Korean Peninsula stabilizes in the future.”
Mr. Chung said the South Koreans believed that their agreements with North Korea would be enough to start a dialogue between Washington and the North. He also said he was carrying additional messages from Mr. Kim to the Trump administration that he could not reveal.
“There was no other specific demand from North Korea in returning to dialogue,” he said. “They only said they wanted to be treated like a serious dialogue partner.”
For Mr. Trump, the overture by North Korea sets in motion a challenging phase that will call on the United States to exercise diplomatic muscles after a long stretch in which the White House relied on economic pressure, backed by threats of military force.
That challenge will be compounded because the State Department’s veteran North Korea negotiator, Joseph Yun, recently announced his retirement from the Foreign Service. Another experienced negotiator, Victor Cha, was recently sidelined when the White House decided not to proceed with his nomination as ambassador to South Korea.
Administration officials are wary of entanglement in a negotiation in which the United States makes concessions — on issues like military exercises or shipments of medical and food aid — only to see the North Koreans renege on their commitments later.
Mr. Trump has said that the United States could talk with North Korea, but “only under the right conditions.” American officials have repeatedly said they can start negotiations with the North only if it agrees to discuss denuclearizing. They have also insisted that the North first take some actions that would convince them of its sincerity.
Another complication is the increased tension between the United States and South Korea, both over Mr. Moon’s exuberant diplomatic engagement with the North and over trade.
Privately, American officials voice frustration that Mr. Moon has responded so readily to the overtures from Mr. Kim. During Vice President Mike Pence’s trip to South Korea for the Olympics, for example, Mr. Moon sought to broker a meeting between Mr. Pence and North Korean officials — seating him a few feet away from Mr. Kim’s sister, Kim Yo-jong, during the opening ceremony.
Mr. Trump’s announcement of tariffs on steel could be an even greater source of friction. South Korea is the third-largest exporter of steel to the United States, accounting for nearly 10 percent of all exports.
While the president has floated the idea of excluding Canada and Mexico from the tariffs, provided they agree to renegotiate the North American Free Trade Agreement, he has said nothing about South Korea. Other administration officials said South Korea was among the worst offenders in terms of dumping steel into the American market.
Mr. Trump is already demanding that South Korea overhaul its free trade agreement with the United States. Some in the administration have urged Mr. Trump to delay punitive trade measures while South Korea and the United States jointly deal with the North Korea issue.
Defense Minister Itsunori Onodera of Japan, which has steadfastly supported the Trump administration’s tough approach to sanctions against North Korea, struck a note of caution about the North’s interest in negotiations.
“While talking about nuclear abandonment several times, it turned out that North Korea didn’t halt its nuclear development in the past,” Mr. Onodera said. “We need to carefully assess if this North and South dialogue will really lead to the abandonment of nuclear and missile development.”
China, which has pushed for direct talks between the North and Washington for many months, welcomed the South Korean statement. Geng Shuang, a Foreign Ministry spokesman, said China hoped “the relevant parties can seize the current opportunity” to work toward “politically resolving the Korean Peninsula issue.”
One Chinese expert on North Korea characterized its reported offer as “concessions that are dramatic and significant.”
“It will be hard for the U.S. government to resist,” said the expert, Cheng Xiaohe, of Renmin University in Beijing.
But Evans J. R. Revere, a former State Department official who was involved in previous negotiations with North Korea, was less impressed. He said the formula of denuclearization for security guarantees had “been the basis of several sets of talks” between the two countries in the past.
Even so, Mr. Revere said the Trump administration would be hard-pressed to reject the North’s proposal without making it appear that Washington — not the North — was the problem.
“With these developments, the door seems wide open to a U.S.-North Korea exploratory conversation if both sides want one,” he said.