IF ANY international norm can still be called uncontroversial, it is the stricture against cross-border aggression by one sovereign state against another. Certainly any failure to enforce it in one place invites violations elsewhere. That is why Vladi­mir Putin’s decision to send Russian forces openly into Ukraine in the past 48 hours is a watershed, not a mere “continuation of what’s been taking place for months,” as President Obama understated the case Thursday. If Mr. Putin does not pay a high price for this naked, if still cynically denied, attack on his neighbors, the precedent could sow instability far and wide — from the Baltic Sea, ringed by small, free states with large Russian minorities, to the South China Sea, dotted with islands that China covets but other countries claim.

The reasons for Mr. Putin’s escalation, after months of destabilizing Ukraine through more covert means, may be only guessed. Ukraine’s military has made gains against Russian-instigated “separatists” in two key cities, Luhansk and Donetsk, and Mr. Putin may have felt that he could not abandon them without incurring political risk in Moscow. The Russian army’s move on Novoazovsk, well to the south of these contested areas, relieved the pressure on them — and perhaps foreshadows seizing a land corridor to Crimea, which Mr. Putin absorbed through force and chicanery six months ago but has struggled to resupply by air and sea since. Mr. Putin’s strategic goal could be even grander: the takeover of southeastern Ukraine, which he calls “New Russia,” and its incorporation into his ballyhooed Eurasian Union.

What is evident is that Mr. Putin cares little for diplomatic “off-ramps,” as the West calls the various face-saving solutions it has dangled since Mr. Putin first began his squeeze on Crimea, and to which Mr. Obama alluded yet again Thursday. To the contrary: Sending his own regulars to seize Ukrainian territory suggests that he would rather risk further conflict with the West than see his minions go down to defeat in Donetsk, Luhansk and elsewhere.

There may be some in Washington who conclude from this that Mr. Putin’s interest in Ukraine will always be greater than that of the United States, so pressure or sanctions can’t work — and might even be counterproductive, given the need for Russian cooperation on other matters such as Iran’s nuclear program. If the issue were only Russia’s neighborhood, we would still disagree, vehemently, but we would understand the logic.

But given the global repercussions of this struggle, the United States and its allies cannot afford to let Mr. Putin break the rules. It is time to hit Russia with the full brunt of financial sanctions, to supply Ukraine with the arms and intelligence it needs to defend its territorial integrity (which Russia itself once pledged to respect), to halt all military sales to Russia by Western nations — and to bolster the neglected North Atlantic Treaty Organization. Mr. Obama made little effort Thursday to explain or defend the “broader principle” that he said is at stake in Europe. Nations around the world that rely on U.S. leadership and its commitment to the rule of law can only hope that he brings more passion to the cause at what deserves to be a historic NATO summit in Wales next week.