But behind the scenes, officials have been cautiously discussing the conditions under which the United States could reengage in direct dialogue with North Korea. One idea, which South Korean President Moon Jae-in suggested before the North's latest missile launch, is that a deal could be struck to return the three Americans imprisoned there in exchange for a resumption of talks.
Moon publicly floated that idea for the first time last Friday at a forum hosted by the Center for Strategic and International Studies.
"President [Donald] Trump himself also mentioned that under the right conditions we can have dialogue with North Korea. . . . So that raises the question, what are the conditions that enable us to engage in dialogue," Moon said. "For example, maybe we can start dialogue with North Korea when North Korea promises to stop its nuclear and missile provocations. Or another example could be when North Korea releases the three American citizens it is currently detaining. Maybe that could be a start to the right conditions for dialogue."
Moon cautioned that the conditions for dialogue were not clear at this moment. He also said that the United States and its allies should not give North Korea any concessions in exchange for beginning talks, such as reducing the scope or scale of U.S.-South Korean military exercises, as the Chinese have suggested. But experts said his idea of trading dialogue for American hostages likely wasn't a coincidence.
"The Americans being held hostage, that's a new precondition that hadn't really been put forward before," said Anthony Ruggiero, senior fellow at the Foundation for the Defense of Democracies. "Either he was floating it, or it was something that was mentioned in the meeting with President Trump."
A senior administration official confirmed that Trump and Moon discussed the hostages and said that Trump is personally committed to making progress on that issue, especially since the return and subsequent death of Otto Warmbier, the American college student who spent nearly 18 months detained in North Korea.
The official declined to say if such a precondition was actively being explored as a way to get to the table with the Kim regime, but said, "It will be tough for there to be substantive talks while there are American prisoners in that country. You can interpret that however you want."
The Trump administration has been intentionally ambiguous about exactly what conditions would be acceptable for a resumption of negotiations, officials said. Meanwhile, State Department official Joseph Yun, who negotiated the release of Warmbier and traveled to Pyongyang to retrieve him, maintains the only functioning diplomatic channel with the Kim regime.
What happens after the two sides sit down at the table is another matter entirely. Moon said that while a freeze of North Korea's nuclear and missile programs could be a way into negotiations, the way out must be a total dismantling of those programs according to North Korea's previous commitments.
"In a theoretical way, that is correct, but the North Koreans have been very clear that they don't want to discuss denuclearization," said Ruggiero. "The North Koreans want a freeze as the way in and us accepting them as a nuclear state as the door out."
To be sure, Pyongyang's latest provocation makes any thought of sitting down with North Korea more difficult. The Trump administration reacted to the ICBM launch with a full-court press to persuade allies and adversaries alike to drastically ramp up pressure on the Kim regime and its enablers.
Trump tweeted that he no longer is counting on Chinese cooperation while Secretary of State Rex Tillerson is calling for "global action" to squeeze North Korea's economy like never before. The U.N. Security Council is convening this afternoon to seek consensus on new sanctions.
The Trump administration is moving toward the "maximum pressure" strategy it announced earlier this year. In the coming days and weeks, there could be more sanctions on Chinese businesses and individuals who help North Korea's illicit activities.
The theory is, if the pressure gets strong enough, the Kim regime may change its calculus.
"You are trying to make North Korea choose between their nuclear weapons and regime stability," said the Heritage Foundation's Bruce Klingner.
The problem with that strategy is that there may be no level of pressure that gets Kim Jong Un to change course, especially without Chinese government buy in.
"It ain't gonna work," said former nuclear negotiator Joel Wit. "Diplomacy is the only option now that is not a dead end."
If and when Trump administration officials reach the point where they have ramped up the pressure as much as they can, they will have no other option but to talk to the North Korean government. And even if those talks are fruitless, at least they might be able to bring three more Americans home in the process.