WASHINGTON — As worrying as North Korea’s nuclear advance is for America, the increasingly realistic threat of an atomic warhead striking a U.S. city might be even more unnerving for South Korea and Japan. So much so that the United States is considering new ways to flex its nuclear muscle to defend its vulnerable allies as they ponder if they’ll one day need atomic arsenals of their own.

For decades, the United States has defended South Korea and Japan, the nations most directly threatened by the North’s missiles and massive conventional forces, through an extended “nuclear umbrella.” The basic premise is that an attack on either ally risked a devastating American response. It’s a U.S. commitment that has guided the actions of American friends and foes alike.

Pyongyang’s emerging capabilities are upsetting all calculations. The North this weekend exploded its strongest-ever nuclear weapon and in July tested a pair of intercontinental ballistic missiles that might soon be able to threaten the entire American mainland.

Now that the United States faces its own threat of North Korean retaliation, the most pressing security question of the next years could be: Would Washington risk San Francisco for Seoul?

“It’s the core dilemma of extended deterrence for allies in the nuclear era: Will the U.S. actually risk one of their population centers for our defense?” Sheila Smith at the Council on Foreign Relations said. “It’s hard to believe the answer is yes.”

Speaking to The Associated Press on Tuesday, former South Korean Foreign Minister Yoon Young-kwan acknowledged that North Korea’s more powerful bombs and further-reaching missiles are sparking debate about his country’s long-term security strategy.

“Worries have begun to appear,” he declared of the U.S. commitments, and said a growing minority of South Koreans want Washington to redeploy short-range nuclear weapons that were withdrawn from the country in the early 1990s. Others question if South Korea should have nukes of its own.

Song Young-moo, defense minister of Seoul’s currently dovish government, on Monday suggested bringing back the U.S. nuclear weapons was worth consideration. He reportedly discussed the matter with Defense Minister Jim Mattis last week.

The Pentagon declined to outline its position.

“We work closely with our allies but it is always inappropriate to discuss the locations of our nuclear arsenal, or the topics of closed-door discussions,” Col. Rob Manning, a spokesman, said.

Japan, the only country to have suffered nuclear attacks, is more strongly opposed to having atomic weapons. Its defense planners are weighing if they need an offensive, conventional missile strike capability to respond to a North Korean attack. A nuclear leap isn’t unimaginable. From its nuclear energy program, Japan sits on a stockpile of reprocessed plutonium that could be turned into the material for thousands of bombs.

For as long as North Korea couldn’t strike the U.S. with nuclear weapons, both allies felt assured that the promise of an overwhelming American military response would deter the communist country. Now, the North’s technological progress is adding to insecurities compounded by President Donald Trump’s sometimes lukewarm support for defending U.S. allies under his “America First” agenda.

No one knows how North Korea will use its newfound nuclear capabilities.

It could adopt a policy of deterrence, similar to that of the world’s established nuclear powers, keeping its arsenal as a defense against what it believes are American designs to overthrow leader Kim Jong Un. It could use the weapons offensively, although that would risk devastating nuclear retaliation.

More likely is a policy somewhere in between.

As it assesses the rest of the world’s reluctance to engage in nuclear crossfire, the North could act more aggressively with its conventional forces against South Korea. Or it could simply leverage its atomic arsenal to win international concessions in negotiations.

Under any approach, Trump and future U.S. commanders in chief will have a very persuasive argument for why the North shouldn’t directly attack the United States: American military superiority. Trump last month warned of “fire and fury” if the North threatened the U.S.; Mattis this weekend raised the specter of the “total annihilation of a country.”

South Korea and Japan can present no picture of apocalyptic retaliation by themselves — which adds to their current vulnerability. Despite Mattis’ declaration that such American promises are “ironclad,” Pyongyang’s potential ability to strike an American city with nuclear weapons will naturally affect U.S. strategic thinking.

Would Washington come to South Korea’s aid and take on such a risk if the North shells a southern island with artillery as it did in 2010? What if North Korea, with the world’s largest standing army, crosses into the South?

“South Korea may face the most complex strategic environment in Asia,” write Sung Chull Kim and Michael D. Cohen, editors of a new collection of scholarly essays titled “North Korea and Nuclear Weapons: Entering the New Era of Deterrence.” ”A very weak but heavily armed North Korea, despite being no match for the South Korean military, threatens Seoul with imminent destruction.”

Kim and Cohen write of the North’s enhanced threat creating a “perceived commitment deficit from Washington.”

Such assessments are driving the Trump administration to reassure its allies.

On Tuesday, Trump said he would allow Japan and South Korea to “buy a substantially increased amount of highly sophisticated military equipment from the United States.” The tweet followed Trump giving South Korean President Moon Jae-in an “in-principle approval” for weapons with less restrictions and more powerful warheads.

But sending U.S. nuclear weapons back to South Korea would be a more drastic step, contradicting the efforts of multiple administrations to “denuclearize” the Korean Peninsula.

Twenty-six years ago this month, in the hopeful aftermath of the Cold War, President George H.W. Bush announced the unilateral withdrawal of all land-based and sea-based tactical nuclear weapons, including from South Korea. He then pulled all air-delivered nuclear bombs from the South in part because officials believed they were no longer needed for an effective defense. That was years before the North demonstrated its nuclear prowess with a first explosion in 2006.

Redeploying the weapons to South Korea wouldn’t dramatically change the strategic balance, as the U.S. has nuclear assets on submarines that can operate off North Korea’s coast. However, doing so could provide the South with a renewed sense that the U.S. would use its nukes in a crisis.

Such action would provoke extreme objections from key regional powers, China and Russia, who would likely accuse the U.S. of fueling an arms race. And it’s hardly universally supported among U.S. policy makers or South Koreans.

“It is a bad idea,” said James Acton, co-director of the nuclear policy program at the Carnegie Endowment for International Peace. He said it wouldn’t significantly strengthen nuclear deterrence and might spark protests in South Korea that weaken its U.S. alliance.

If the Trump administration were to return U.S. nuclear weapons to the peninsula, they probably would be bombs for delivery by what the Pentagon calls “dual capable” aircraft. These include F-16 and F-15 fighter jets configured to perform either nuclear or conventional attack missions. Security requirements to safely store and maintain the weapons also would require upgrades or additions to U.S. military facilities in South Korea.