THE OBAMA administration suffered a foreign policy setback last week when three European allies — Germany, France and Italy — decided to join a fourth, Britain, as shareholders in a new Chinese-sponsored multilateral development agency for Asia.

When Beijing first proposed the Asian Infrastructure Investment Bank (AIIB) in 2013, Washington viewed it, not unreasonably, as a Chinese attempt to set up a rival to the U.S.-led World Bank, with the goal of expanding the influence of the People’s Republic across the region. A foreseeable negative consequence of a successful AIIB could be project funding ungoverned by the environmental and anti-corruption safeguards that World Bank borrowers must meet. The fact that four key European allies found it advantageous to join, despite U.S. insistence, speaks volumes about the ebb and flow of American influence in a region toward which President Obama had promised to “pivot.” Indeed, the Europeans’ moves make it more likely that South Korea and Australia will feel compelled to join the Chinese-led agency, leaving the United States and Japan on the outside looking in.

For now, the AIIB is more about symbolism than substance. With an initial capital of just $50 billion, one third that of the Japan-led Asian Development Bank, and none of the World Bank’s expertise or institutional heft, it’s unclear how much of a dent the new bank could make in the region’s multi-trillion-dollar needs for roads, dams, bridges and ports. Its governance structure remains ill-defined and, potentially, a subject of controversy if and when the projects it backs start to have negative environmental or social consequences. (Here’s hoping that the myriad nongovernmental organizations that regularly criticize the World Bank’s practices and procedures do not give China’s bank a pass.)

The question for Washington now is how to respond. This turn of events might have been avoided if Congress had approved the Obama administration’s request for International Monetary Fund financing that included a formula for greater Chinese power at the IMF. In that sense, Washington has itself to blame. Yet approving the IMF money now would probably be too little too late to reverse the AIIB’s momentum — and it’s not clear that Beijing would have been appeased by a greater IMF role. Nor does the United States have much to gain by joining the AIIB itself, on the off chance Congress would approve. Some have suggested this would enable Washington to shape the institution from within; better, though, to see what impact the Europeans have before lending AIIB a U.S. imprimatur.

Mr. Obama’s best bet is to redouble efforts to shore up World Bank funding, and to win congressional approval for the Trans-Pacific Partnership (TPP) free-trade arrangement, which would tie the United States and East Asia more closely together, while establishing a regional economic framework built on Western-style economics rather than Chinese mercantilism. If, as the administration suspects, the AIIB represents an aggressive Chinese geopolitical thrust, then TPP is the appropriate way to parry it.