On the eve of Russia’s invasion of Ukraine, Vladimir Putin issued a nuclear warning. He admonished that “anyone who tries to interfere with us…must know that Russia’s response will be immediate and will lead you to such consequences as you have never before experienced in your history.” In case anyone misunderstood his warning, he added that Russia remains “one of the most powerful nuclear powers” with “certain advantages in a number of the latest types of weapons” and stated that “no one should have any doubt that a direct attack on Russia will lead to defeat and dire consequences for a potential aggressor.” A few days later, he upped the ante further with the public announcement of a Russian nuclear alert.

The US cannot overlook these chilling threats. They are part of a deliberate strategy to advance Russia’s revisionist political and military goals. Countering them will require the US and its friends to tailor both their conventional and their nuclear postures to the emerging danger—not only in the current crisis with Russia but also to prepare for the possibility that China might follow the same playbook in a future war over Taiwan.

Mr. Putin’s unusually explicit rhetoric has sent a clear message to the West: Stay out of my attack on a third party or risk nuclear conflict. Having bolstered in recent years its arsenal of nuclear weapons that can evade missile defenses and hit targets in Europe and the US, Russia is attempting to use these forces as a shield for conventional aggression. Mr. Putin is betting that despite the conventional military might of the US and its allies, they will shrink from confrontation at least partly out of fear of nuclear escalation.

This approach to nuclear deterrence calls into question the often-cited logic of mutually assured destruction, or “MAD.” This traditional notion assumes that mutual nuclear vulnerability—that is, a situation in which both sides have nuclear forces that can inflict significant retaliation on the other, even after suffering a nuclear first strike—can actually stabilize world politics and make conflict between nuclear adversaries, even over third parties, less likely. Under this condition, the risks of nuclear escalation become so dangerous and so inescapable that countries will hesitate even to provoke a crisis, much less to fight wars. Many credit MAD with keeping the Cold War cold.

The problem is that precisely because all-out nuclear war would be so costly for both the US and Russia, Mr. Putin likely believes it won’t happen. As a result, he may feel relatively safe engaging in conventional aggression or even limited nuclear use below that threshold—demonstration strikes, for example, or attacks on military targets—without much risk of a Western response. In general, he appears to believe that Russian nuclear weapons provide cover for Russian aggression, while American nuclear weapons don’t provide reciprocal freedom to respond, perhaps because the US is less invested in defending the status quo than Mr. Putin is in challenging it. Pakistan has honed exactly this strategy against India, and now a revisionist Russia is adopting it too.

Russia has longstanding grievances with the geopolitical status quo, including most notably the expansion of NATO after the humiliating contraction of the Soviet empire. These resentments, combined with a serious miscalculation about how the West would respond to his invasion, may have emboldened Mr. Putin to make nuclear threats, despite the powerful US arsenal. Ultimately, however, Russia doesn’t want to get into a nuclear war with NATO. It just wants NATO to stay out of Russia’s conventional war against Ukraine.

Unfortunately for the US, Russia isn’t the only opponent that could use its nuclear arsenal as a shield for conventional aggression against third parties. China is in the midst of modernizing its nuclear forces, building better nuclear weapons in larger numbers than it ever has before. These include both long-range forces that can threaten the US and medium-range nuclear weapons well-suited to limited attacks on US military targets and allies in the western Pacific.

China’s arsenal likely will remain significantly smaller than those of both Russia and the US for some time. Nevertheless, Beijing is pushing Washington into a state of deeper mutual nuclear vulnerability. As with Russia, the U.S. would find an all-out nuclear war with China extremely costly, and both sides will have strong incentives to avoid it. Yet this strategic nuclear stalemate is unlikely to be stabilizing given that China, like Russia, is deeply dissatisfied with the status quo, especially over Taiwan.

A more robust nuclear arsenal may not make China more cautious. Instead it may give China confidence that if it conventionally challenges US friends or allies in the region, the US can’t simply lean on its nuclear status to get China to back down.

By attempting to neutralize the US ability to make credible nuclear threats in a crisis, China may believe it can keep the fight conventional—which would play to China’s strengths. China overmatches Taiwan conventionally, just as Russia does Ukraine. Likewise, Beijing cares about Taipei’s status more than Washington does. Again, an opponent that has little desire to fight a nuclear war with the US may nevertheless rely on its nuclear forces to stiff-arm an American conventional response.

Russia and China have distinct relationships with the US, but they present a common problem: The US seeks to maintain credible commitments to allies and friends in the two regions. But how can it do this when conventionally strong, nuclear-armed US opponents seek to revise the status quo through the use of force?

As Ukrainian resistance has already demonstrated, robust conventional forces are a critical part of the answer, both on NATO’s eastern flank and along the first island chain in East Asia. An adversary’s nuclear threats aimed at keeping the US out of a conventional fight will matter much less if allies can make that fight conventionally costly for the opponent, regardless of whether, when or how the US intervenes. The key is to provide allies with defensive capabilities that don’t threaten adversaries unless they attack.

Especially for Taiwan, that means investing less in high-prestige aircraft and ships and more in mines, submarines, drones, missiles and air defenses that can impose heavy costs on a Chinese attempt to cross the strait. Improving the island’s economic and military resilience in the event of air and missile attacks is also important, as is publicly signaling these measures.

Similarly, the US should focus its own conventional posture on the goal of denying Russia and China the ability to conduct rapid military campaigns that revise the territorial status quo. In coordination with allies, the US should prioritize intelligence assets, forward deployment of munitions and equipment, and investment in weapons systems such as nuclear-powered attack submarines and penetrating bombers that have the best chance of surviving a fight with a highly capable adversary. Even in the presence of large nuclear arsenals, these conventional capabilities will remain vital to keeping the peace against opponents who may otherwise believe that nuclear weapons give them cover for aggression.

The US nuclear arsenal remains the ultimate backstop of its alliance commitments. Distasteful as it is to contemplate, having the ability to threaten limited nuclear attacks, particularly against military targets, remains important for deterring Russia and China, both of which are readily deploying such weapons. The key is to signal prior to any war both that the US has no desire to initiate conflict and that threats of nuclear escalation won’t force the US to back down. The presence of the American arsenal can also help reassure allies that the US will defend them, making them less likely to seek nuclear weapons of their own.

Caitlin Talmadge is associate professor of security studies in the School of Foreign Service at Georgetown University and the author of “The Dictator’s Army: Battlefield Effectiveness in Authoritarian Regimes.” She received her PhD from MIT and is a research affiliate of the MIT Security Studies Program.