Above all, the officials said, the Trump administration will resist efforts by the North to drive a wedge between the United States and its ally. North Korea, they said, has a long history of using such overtures to sow dissent between South Korea and the United States, particularly at times, like now, when the countries have governments with divergent politics.
The White House also reiterated that Mr. Trump would continue to defy Mr. Kim, regardless of any diplomacy underway. The press secretary, Sarah Huckabee Sanders, defended the president’s Twitter message late Tuesday about Mr. Kim in which he said, “I too have a Nuclear Button, but it is a much bigger & more powerful one than his, and my Button works!”
People, Ms. Sanders said on Wednesday, should question Mr. Kim’s mental fitness, not Mr. Trump’s.
“Our policy with North Korea has not changed,” Ms. Sanders added. “We’re fully committed to continuing to apply maximum pressure and working with all of our partners in the region, including South Korea, who we have a better relationship with now than ever before.”
But that relationship will be tested by the opening to the North, according to officials and outside analysts. The Trump administration already has a strained relationship with South Korea’s progressive president, Moon Jae-in, who has called for dialogue with the North since his inauguration in May.
After North Korea tested a nuclear bomb in September, Mr. Trump said on Twitter, “South Korea is finding, as I have told them, that their talk of appeasement with North Korea will not work, they only understand one thing!”
During Mr. Moon’s first visit to the White House, Mr. Trump delivered a harsh critique of South Korea’s trade surplus with the United States. Negotiating teams from the two countries are scheduled to meet on Friday in Washington to begin discussing possible changes to the five-year-old Korea Free Trade agreement, which Mr. Trump has derided as “not exactly a great deal.”
“It’s a dilemma for the administration,” said Michael J. Green, who was the top Asia adviser to President George W. Bush.
“The default position of the United States should be to support North-South dialogue,” he said. “At the same time, they are understandably nervous about the Moon government, which has some members who are too breathless about the prospects for dialogue.”
Mr. Green said he was guardedly optimistic because the Trump administration’s strategy of imposing sanctions on North Korea had shown some signs of success, which would give South Korea confidence to stick with the United States.
South Korea’s public, he said, also remained suspicious of the North, which he said would limit the scope of Mr. Moon’s diplomats to make overly generous concessions.
Diplomats said it was important that South Korea appear to be in lock step with the United States. That would be easier to do, they said, if the talks remain focused on relatively narrow issues, like security at the Winter Olympics.
“It is fine for the South Koreans to take the lead, but if they don’t have the U.S. behind them, they won’t get far with North Korea,” said Daniel R. Russel, a former assistant secretary of state for East Asian and Pacific Affairs in the Obama administration. “And if the South Koreans are viewed as running off the leash, it will exacerbate tensions within the alliance.”
Mr. Russel and Mr. Green both said Mr. Trump would be a wild card in the delicate détente. So far, the president has shown skepticism about the opening, although he has not dismissed it. “Rocket man now wants to talk to South Korea for first time,” Mr. Trump tweeted on Tuesday. “Perhaps that is good news, perhaps not — we will see!”
But the president has not hesitated to weigh in with provocative tweets if he judges that events have gone badly.
In the fall, he spent weeks praising President Xi Jinping of China for putting increased economic pressure on North Korea. Then, last month, Mr. Trump abruptly shifted his tone after reports that Chinese ships were transferring fuel to North Korea.
“Caught RED HANDED,” he wrote on Twitter, “very disappointed that China is allowing oil to go into North Korea. There will never be a friendly solution to the North Korea problem if this continues to happen!”
On Tuesday, Mr. Trump took shots at Pakistan and the Palestinian Authority, in addition to North Korea. Those tweets reverberated with both governments and could cause lasting damage. His message about his and Mr. Kim’s nuclear buttons — coming on the day that the North made contact with the South — left diplomats shaking their heads.
“This is where his Twitter account can cause an inflection point in the relationship,” Mr. Green said.
He said it would be vital for Mr. Trump’s national security and intelligence advisers to brief him on the diplomatic opening in a way that did not nurture his suspicions.
But the president’s aides have little control over outside forces, like Mr. Kim’s assertion in his New Year’s Day speech that he had a nuclear button on his desk, and that all of the mainland United States was in range of a North Korean nuclear strike.
That was the claim that provoked Mr. Trump’s tweet.
“Calling his nuclear arsenal too small is not the best way to persuade him to constrain that arsenal,” Mr. Russel noted, referring to Mr. Kim.
Referring to South Korea, Mr. Russel asked, “Who is going to bear the brunt of this taunt?”
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