American fighter jets scrambled to intercept Russian bombers earlier this month near the island of Guam. It was the first time since the end of the Cold War that the Kremlin sought to provoke a U.S. response. It likely will not be the last. Fueled by revenues from energy exports, Russia appears bent on ratcheting up tensions.

But don’t expect the next foray to take place over international waters. Vladimir Putin laid bare his ambitions at the St. Petersburg International Economic Forum in June by calling for a “new international financial architecture” to provide a base for economic development. Russia’s next move is to challenge U.S. supremacy in world financial markets.

The notion of nudging America off its central perch in global economic affairs hardly seems plausible. But Russia’s leader strikes a chord with other emerging-market economies—Brazil, China, India—when he describes current monetary and financial arrangements as “archaic, undemocratic and unwieldy.”

Given the recent turmoil in world financial markets, Mr. Putin can expect heightened interest in his pitch for new regional alliances “based on trust and mutually beneficial integration” versus continued dependence on global institutions like the International Monetary Fund. Both Europe and Asia blame U.S. credit woes for their own unsettled markets. And newly independent nations on the periphery of established trade and security blocs have their own reasons to align with powerful patrons.

Mr. Putin even suggests that central banks should begin to hold reserves in a wider selection of currencies than dollars and euros in recognition of the “existing balance of power.” It’s hard to miss the implication: the ruble as a global reserve currency.

Is the man serious? The only reason the European Central Bank, say, or China’s central bank, might hold reserves in rubles would be to pay for purchases from Russia. Today it is possible to buy Russian oil and gas using dollars or euros. The leading market exchanges for conducting international energy transactions are located in New York and London. But that is why officials at the White House, the Federal Reserve and the U.S. Treasury should be scrambling right now.

Mr. Putin is more than serious. He is determined to establish a world-class oil exchange on Russian territory and shift energy business away from existing global financial centers. A new facility is being readied in St. Petersburg’s historic Bourse—an imposing, white-colonnaded Greek Revival building that dominates the majestic sweep of the Strelka, or Spit, of Vasilievsky Island in the Neva delta and which is visible from the Winter Palace—that will open to market traders within months and where transactions will be denominated in rubles.

It’s a daring gambit and it constitutes no less than a demand for new international monetary arrangements on the scale of the post-World War II Bretton Woods agreement. “The global economy has experienced a transition,” Mr. Putin notes pointedly. “Fifty years ago, 60% of world gross domestic product came from the Group of Seven industrial nations. Today 60% of world GDP comes from outside the G7.”

Mr. Putin’s plan to confront the privileged global role of U.S. currency resonates with Russians eager to recapture nationalist pride. Lampooning the sickly American dollar is popular with members of the Kremlin-financed youth group Nashi (meaning “ours”). And it potentially accommodates the burgeoning economic aspirations and swelling egos of Russia’s partners in the Shanghai Cooperation Organization: Kazakhstan, Kyrgyzstan, Tajikistan, Uzbekistan and China.

China, like Russia, bristles at its second-tier status within the global financial architecture. Harangued by the U.S. over exchange-rate policies, China has recently been flexing its monetary muscle by hinting that it might dump a portion of its considerable dollar reserves. The prospect of such a shock to the U.S. economy in the midst of a housing slump threatens to bring the whole edifice crashing down. Throw in statements of support from oil-producers Venezuela and Iran, and you have the makings of a devastating dollar rout.

If Russia insists that its energy clients pay in rubles, we cannot expect our allies to strenuously resist. Europe purchases nearly 30% of its energy from Russia. Rising energy demand in Asia will likewise boost demand for rubles as Russia targets China, India and Japan. Last month, Japan quietly acquiesced to Iran’s request that it switch from dollars to yen in payment for Iranian oil.

Can U.S. leaders and financial authorities meet the challenge from the Kremlin? Is America prepared to offer its own proposals for establishing more stable currency and financial conditions for global trade? Or are we just interested in protecting our turf?

The next Bretton Woods should be launched as an earnest initiative from the nation that gave birth to democratic capitalism. Not as an act of aggression from a pumped-up Russian pretender.