“I think the problem we have right now is no one wants to blink or look weak in any way,” said Melissa Hanham, a senior research associate at the Middlebury Institute of International Studies in Monterey, Calif. She added: “The positions of the United States and North Korea are extremely far apart.”
“If it were easy,” she said, “we would have done it already.”
Bridging that gap has fallen largely to Mr. Tillerson, a former chief executive of the oil giant Exxon Mobil, with no experience in diplomatic negotiations or with North Korea in particular. He must contend not only with the North’s brash 33-year-old leader, Kim Jong-un, but also an American president prone to issuing impromptu threats.
Speaking in Beijing on Saturday, Mr. Tillerson said he was trying to cool the bellicose rhetoric over the standoff but skirted any direct criticism of Mr. Trump. “I think everyone would like for it to calm down,” he said.
The president undercut Mr. Tillerson the next day, belittling his efforts to start a dialogue. But State Department spokeswoman Heather Nauert asserted again on Twitter later in the day that, “Diplomatic channels are open for #KimJongun for now.”
She added, “They won’t be open forever.”
The North has shown little interest in starting talks, at least not if giving up its weapons is the price of admission. Some analysts argue the North may be waiting until it has finished building a nuclear missile that can hit the United States, which would allow it to negotiate from a much stronger position.
In a personal response to Mr. Trump’s speech to the United Nations General Assembly last month, Mr. Kim said that the president’s threat to “totally destroy” North Korea had “convinced me, rather than frightening or stopping me, that the path I chose is correct and that it is the one I have to follow to the last.”
Many analysts say Washington will have to give up its demand that Pyongyang abandon its nuclear weapons program to get negotiations started.
“If our opening bid is denuclearization, that just seems like a Western fantasy at this point,” said Vipin Narang, an associate professor of political science at Massachusetts Institute of Technology. “What incentive does Kim have to give them up at this point? If that’s our only acceptable end point, I don’t see any way that he willingly gives up his nuclear weapons.”
A more realistic opening goal would be to negotiate a freeze in missile and nuclear tests, said Suzanne DiMaggio, a director and senior fellow at the New America research group who has been involved in unofficial talks with North Korea. Ms. DiMaggio said that such a freeze could be an interim step. “This way it implies that there will be more agreements to come,” she said.
In exchange, Ms. DiMaggio suggested, the United States could discuss scaling back the joint military exercises it holds with South Korea, which are scheduled to resume again in the spring. The North considers these war games threatening, particularly components that target the country’s leadership in the event of war.
The United States could also offer to send fewer B-1B long range bombers on patrols near the Korean Peninsula, to withdraw certain sanctions or to open an embassy in Pyongyang.
But the Trump administration does not appear willing to discuss such concessions without a commitment by Pyongyang to dismantle its nuclear program. North Korea wants the United States to acknowledge that it is a nuclear state, a demand that analysts say would be difficult for any American president to accept.
“That is so inimical to U.S. national security interests,” said Daniel R. Russel, who served as assistant secretary of state for East Asia during the Obama administration. “It would have such a devastating effect on both the international nonproliferation system and on the credibility of the U.S. as an ally, not to mention our relationships with South Korea and Japan, that I view it as unimaginable.”
Mr. Russel argued that the United States should continue to apply pressure through sanctions on North Korea until Mr. Kim concludes he has no choice but to negotiate.
“People are fond of saying that North Korea will never negotiate denuclearization,” he said. “But I think that there’s an important adverb missing, which is that North Korea will never negotiate denuclearization willingly.”
Others said North Korea was uniquely prepared to withstand economic isolation.
“This is a country that didn’t collapse during the height of a famine, and they are doing better now, so you think you are going go squeeze them some more?,” said David C. Kang, director of the Korean Studies Institute at the University of Southern California.
If North Korea refuses to surrender its nuclear arsenal, he said, the United States will have to learn to live with it.
“We did this with Pakistan,” Mr. Kang said, noting Washington tries to limit the scope of the Pakistani arsenal. “There are plenty of countries where we did this. Let’s try to find a way to live with each other without killing each other.”