WASHINGTON — In the four years since President Donald J. Trump’s leader-to-leader diplomacy with Kim Jong-un of North Korea collapsed after a failed meeting in Hanoi, the North’s arsenal of nuclear weapons has expanded so fast that American and South Korean officials admit they have stopped trying to keep a precise count.
North Korea’s missile tests are so frequent that they prompt more shrugs than big headlines in Seoul.
So when President Biden welcomes President Yoon Suk Yeol of South Korea to the White House on Wednesday, only the second state visit of Mr. Biden’s presidency, there will be few pretenses that disarming North Korea remains a plausible goal.
Instead, American officials say, Mr. Biden’s most vivid commitment to Mr. Yoon will focus on what arms control experts call “extended deterrence,” renewing a vow that America’s nuclear arsenal will be used, if necessary, to dissuade or respond to a North Korean nuclear attack on the South.
The emphasis on deterrence is a striking admission that all other efforts over the past three decades to rein in Pyongyang’s nuclear program, including diplomatic persuasion, crushing sanctions and episodic promises of development aid, have all failed. It is also intended to tamp down a growing call in South Korea for its own independent arsenal, on the very remote chance that North Korea would make the suicidal decision to use a nuclear weapon.
The North’s arsenal will hardly be the only topic under discussion during Mr. Yoon’s visit. He and Mr. Biden will also celebrate the 70th anniversary of the alliance between their countries, commitments for more South Korean investment in manufacturing semiconductors and plans to bolster Seoul’s always-fraught relationship with Japan.
But the rapid expansion of North Korea’s capabilities is a subject of perpetual mutual concern for both countries. At a recent security conference held by the Harvard Korea Project, several experts said they believed Mr. Kim’s goal was to approach the size of Britain’s and France’s arsenals, which hold 200 to 300 weapons each.
Mr. Biden and Mr. Yoon are expected to hold out the possibility of pursuing a diplomatic solution toward what a succession of administrations have called the “complete, verifiable, irreversible denuclearization of the Korean Peninsula.” But the North, administration officials say, has declined to respond to a series of public and private messages from Mr. Biden and his aides.
And what seems irreversible now is North Korea’s entrenched and advanced program.
With China expanding its arsenal to 1,500 weapons by around 2035, according to Pentagon estimates, and Russia threatening to use tactical weapons in Ukraine, “this is not an external environment in which it’s easy to have a conversation with North Korea,” said Victor Cha, a professor at Georgetown University who directed policy toward the North during the George W. Bush administration. “They look around their neighborhood and they say, ‘I don’t think so.’”
Mr. Trump vowed “fire and fury like the world has never seen” when North Korea greeted his presidency with missile launches; he ultimately tried the innovative approach of direct diplomacy with Mr. Kim. He emerged at one point predicting that Mr. Kim would begin disarming within six months and declaring at another that the North was “no longer a nuclear threat.” The arsenal just kept growing.
On Friday, North Korea’s foreign minister, Choe Son-hui, repeating a line that has been uttered by her government frequently in recent months, said the North’s status “as a world-class nuclear power is final and irreversible.”
Few experts believe the shift in rhetoric or the threats about first strikes indicate a greater willingness by the North to employ nuclear weapons. The response would be devastating. But gone are the days when American officials thought that the arsenal was a bargaining chip, something to be bartered away for trade deals, or for the string of hotels that Mr. Trump said America would help build on the North Korean beaches.
There was a mistaken belief, said Joseph S. Nye, who oversaw one of the first intelligence estimates of North Korea for the U.S. government, “that they would try to cash in their chips and get something” for the nuclear weapons. But rather than developing the country, he said at the Harvard conference, the North’s highest goal was “to preserve the dynasty,” and that meant holding on to the arsenal, and expanding it.
North Korea’s new confidence in expanding the arsenal, American officials said in interviews, is partly explained by a change in the relationship with China. Previously, the United States worked with Beijing — the supplier of critical energy and trade to the North — to rein in the country. In the mid-2000s, the Chinese even hosted the so-called six-party talks — North Korea, along with Japan, Russia, the United States and South Korea — to resolve the nuclear issue. When Pyongyang conducted nuclear tests, Beijing often voted for sanctions, and imposed a few.
Now, rather than view North Korea as an unruly, angry neighbor, China has welcomed it, along with Russia and Iran, as part of what White House officials call a coalition of the aggrieved. While Chinese officials presumably fear North Korea’s nuclear tests could go awry, creating a radioactive cloud, it appears perfectly happy to have the North unsettling the United States and its allies with regular missile tests.
Pyongyang’s most recent tests of intercontinental ballistic missiles — including one powered by solid fuel, which makes it quick to roll out of hiding and launch — suggest that North Korea can now almost certainly reach American territory, even if its ability to hit specific targets is imprecise. And over the past year, the North has enshrined its nuclear capability in its laws and started talking about its first-strike capabilities, rather than casting its arsenal as purely defensive.
On March 27, North Korea also released photos of Mr. Kim inspecting Hwasan-31, a small standardized nuclear warhead kit that can be mounted on its various nuclear-capable missiles and drones.
If the module was a real thing, the photos mean that the North is showing off an ability to mass-produce standardized nuclear warheads, said Hong Min, an expert on North Korean weapons at the Korea Institute for National Unification in Seoul. Mr. Kim has also called for mass-producing nuclear warheads for an “exponential” increase in the country’s nuclear arsenal. Last month, he ordered his government to step up the production of weapons-grade nuclear materials.
South Korean officials said that some of the North’s claims, like the purported capabilities of its underwater drones and supersonic missiles, were exaggerated. The reaction in Washington and Seoul has been to vow to strengthen their alliance — made easier by the fact that Mr. Yoon takes a far more hawkish view of how to deal with the North than did his predecessor, Moon Jae-in, who visited Mr. Biden in May 2021.
So the two leaders are expected to speak at length, publicly, about “extended deterrence,” with Mr. Biden offering more regular, visible visits of nuclear-armed submarines and aircraft to South Korea, bolstering the recently reinstated and expanded joint military exercises. (The exercises were variously suspended and scaled down under Mr. Trump.)
Kim Tae-hyo, a deputy national security adviser for Mr. Yoon, said that a top agenda item at the summit was how to boost South Korean confidence in Washington’s commitment to protect its ally with its nuclear umbrella. But Korean officials say that is more dependent on their confidence in the sitting American president — and whether, in the midst of a North Korean attack on the South that employed tactical nuclear weapons, Washington would be willing to take the risk to enter nuclear combat.
Mr. Biden’s words at a news conference on Wednesday will be picked apart for what they may, or may not, say about his determination to take the risks of nuclear engagement.
A new cyberinitiative will also be announced: The North funds the nuclear program with thefts of cryptocurrency and attacks on central bank reserves, and the South, though it rarely discusses it, has developed a skilled offensive cybercorps loosely based on the U.S. Cyber Command.
Outsiders will also be looking for signs of temporary or permanent damage from the leaks of Pentagon and C.I.A. documents in recent weeks that made clear the United States was listening in on top South Korean national security officials as they debated whether to send artillery rounds to Ukraine. The revelation was highly embarrassing for Mr. Yoon, because it suggested an absence of trust by his biggest ally.
But officials say they believe Mr. Yoon will move past it, celebrating cultural ties with the United States and booming investment by South Korean companies in semiconductor plants.
There is one thing South Korean officials say they will not ask for: a return of American tactical nuclear weapons to their country. They were withdrawn in 1991.
Mr. Yoon’s aides say they do not want them back.
David E. Sanger reported from Seoul and Washington. Choe Sang-Hun reported from Seoul.