President Trump listens during a meeting about immigration with Republican senators at the White House on Thursday. (Jabin Botsford/The Washington Post)

President Trump’s taunting tweet this week raising the specter of nuclear war with North Korea sparked fresh concerns in the Pentagon, at the State Department and even in the White House about whether a carefully calibrated strategy to compel the rogue state into negotiations can survive the impulses of both countries’ leaders.

The presidential pronouncement, as most of his tweets do, caught West Wing aides by surprise, as well as allies in Asia, who wondered whether it was merely an unscripted musing or a sign of a growing rift between the United States and South Korea.

U.S. policymakers had assured their counterparts in Seoul that they would tamp down bellicose rhetoric in the run-up to next month’s Winter Olympics, hosted by South Korea in PyeongChang. Was the United States suddenly shifting course?

But Trump administration officials said that there has been no shift and that the president’s language simply reinforces the government’s strategy of “maximum pressure” to address the rising threat from North Korea. As part of that plan, U.S. military commanders have been readying potential actions against North Korea, short of preventive war, that might communicate the United States’ resolve.

The latest episode began Monday, when North Korean leader Kim Jong Un proclaimed in his annual New Year’s Day speech that he kept a nuclear button on his desk and that his arsenal of weapons could hit the entire United States.

North Korea said it would reopen a border hotline with South Korea Jan. 3, hours after President Trump said he has a “bigger" nuclear button than Kim Jong Un. (Reuters)

Then Tuesday evening, one of Trump’s favorite retired generals, Jack Keane, analyzed Kim’s button boast on the Fox News Channel, the television network Trump regularly watches. Roughly 10 minutes later, Trump — who advisers have said is sensitive to appearing weak and relishes having the last word — weighed in by declaring his button to be “much bigger & more powerful” than Kim’s.

Trump concluded his tweet with this: “And my Button works!”

The exchange of playground-style taunts exposed the pitfalls and the promise of Trump’s improvisational involvement in arguably the most dire foreign policy problem his administration faces.

“It’s a reckless, awful thing for any president to say, but of course it’s not real,” said Patrick Cronin, an Asia expert at the Center for a New American Security. Cronin added that national security adviser H.R. McMaster, Defense Secretary Jim Mattis and Gen. Vincent K. Brooks, the senior U.S. commander in Seoul, “are not going to let that kind of attitude determine U.S. actions. They can prevent the rhetoric from becoming a reality.”

Democratic leaders — as well as some Republicans in the national security establishment — condemned Trump’s tweet as dangerously belligerent and cavalier. “This is not a game,” former vice president Joe Biden told CNN in a rare public criticism of Trump. “This is not about, you know, can I puff my chest out.”

Trump administration officials said the president’s tweet, however colorful, was in keeping with the administration’s “maximum pressure” policy, which emerged from a rigorous process involving top officials from the Pentagon, the State Department and intelligence agencies.

President Trump speaks to reporters on the South Lawn of the White House on Friday. (Jabin Botsford/The Washington Post)

“We are leading an international pressure campaign using diplomacy and sanctions,” said one senior administration official who spoke on the condition of anonymity because of the sensitivity of the subject. “The door is open to engagement, but North Korea has to earn it. Missile tests and nuclear tests are not a way of earning it. Each new outrage only makes it worse for North Korea.”

Administration officials have pushed to tighten U.N. sanctions on North Korea and pressed the U.S. military to come up with unilateral actions short of war to dissuade Pyongyang from intimidating or blackmailing U.S. allies.

In the immediate term, those measures include regular use of U.S. stealth aircraft that can penetrate North Korean air defenses in military exercises and increased interdiction of ships violating U.N. resolutions. More-aggressive measures in the future could include shutting down North Korea’s Internet or firing at North Korean vessels that are harassing fishing boats, according to people familiar with the planning.

The president’s tweets — which are rarely drafted with staff and were not part of the administration’s 2017 policy review — have been a persistent wild card in an otherwise conventional U.S. strategy toward Pyongyang. Some foreign affairs experts said the overall message is similar to what other presidents have conveyed.

“We’ve always said, ‘My button’s bigger,’ though obviously not with that gross double entendre,” said Michael R. Auslin, an Asia expert with the Hoover Institution at Stanford University. “We’ve always warned every country that our military force is stronger, our nuclear force is stronger, so don’t test us.”

But Trump’s critics view the tweets as the product of a thin-skinned and impulsive commander in chief.

“He can’t help himself when he gets news from cable TV,” said Thomas Wright, a senior fellow at the Brookings Institution. “He feels the need to respond to every perceived slight or one-upmanship.”

With tensions on the Korean Peninsula rising and the Olympics only a few weeks away, the tweets’ impact — for good or ill — has been a subject of intense debate in Washington, Seoul and the West Wing, where top advisers often learn about the president’s latest salvo for the first time when it pops up in their Twitter feeds.

Some officials sought to put a positive spin on the president’s messages, saying they have deterred the North Korean regime and its unpredictable leader from threatening moves that could trigger an all-out war. White House officials point to Trump’s vow in August to rain down “fire and fury like the world has never seen” on North Korea if it launched missiles at the United States or territories such as Guam.

“I think the press has underestimated the strategic benefits of some of the rhetoric, or at least should acknowledge that sometimes it’s a double-edged tweet,” the senior administration official said. “Some partners have expressed thanks for the ‘fire and fury’ comment.”

Ian Bremmer, president of the Eurasia Group, said foreign officials he interacts with are increasingly tuning out Trump’s Twitter blasts.

“If you’re a leader in the region, on a scale of one to 10, it’s about a 1.5,” Bremmer said. “They respond to Trump pulling out of the Trans-Pacific Partnership. They respond to Trump pulling out of [the] Paris [climate accords]. That matters. But what Trump’s tweets do is they just reinforce the inconsistency and lack of reliability. Trump’s tweets bear no relationship to policy.”

The impact of the tweets is felt most acutely in South Korea, where officials are terrified at the prospect of war and struggle to get clear direction on U.S. policy from senior officials in Washington.

Nearly a year into his tenure, Trump still has not formally nominated an ambassador to Seoul, leaving South Korean officials without an on-the-ground emissary who could help decode the president’s statements. In the absence of an ambassador, senior officials in Washington have attempted to pick up the slack with more-frequent calls to their counterparts in Seoul.

Trump and South Korean President Moon Jae-in spoke Thursday and agreed to continue the “maximum pressure” strategy, while delaying joint military exercises until after the Olympics to focus on the event’s safety, according to the White House.

Trump plans to send an official delegation to the PyeongChang Games, including high-level current and former government officials, that will be announced in coming days, aides said.

Kim wants to send a North Korean delegation to the Olympics, and there is speculation in the region that he might dispatch his sister, Kim Yo Jong, to lead it. North and South Korean officials are due on Tuesday to hold their first talks in more than two years and plan to discuss the North’s participation in the Olympics.

Earlier this week, Trump cited the talks as proof that his tweets were working.

“With all of the failed ‘experts’ weighing in, does anybody really believe that talks and dialogue would be going on between North and South Korea right now if I wasn’t firm, strong and willing to commit our total ‘might’ against the North,” he tweeted Thursday. “Fools, but talks are a good thing!”

But even Trump’s staunchest backers acknowledge that the tweets provide a potential opening for North Korea’s leadership, which is determined to exploit divisions between Washington and Seoul. These officials note that the North Koreans seldom talk to the Americans and the South Koreans at the same time.

“One of the clear goals of Kim’s New Year’s Day message is to drive a wedge between the United States and South Korea,” said the senior administration official. “It’s very clear. It’s part of their playbook, and that’s what they were attempting.”

One argument against Trump’s saber rattling is that it provides exactly that opening.

“You don’t hear Jim Mattis or Rex Tillerson making this argument,” said Michael J. Green, an Asia expert in the George W. Bush White House. Instead, he said, the two officials have seemed to advocate more of a “containment strategy.”