BRUSSELS — Ignoring direct pleas from the Obama administration, Europe’s biggest economies have declared their desire to become founding members of a new Chinese-led Asian investment bank that the United States views as a rival to the World Bank and other institutions set up at the height of American power after World War II.

The announcement on Tuesday by Germany, France and Italy that they would follow Britain and join the Chinese-led venture delivered a stinging rebuke to Washington from some of its closest allies. It also called into question whether the World Bank and the International Monetary Fund, which grew out of a multination conference in Bretton Woods, N.H., in 1944 and established an economic pecking order that lasted 70 years, will find their influence diminished.

The announcement by Germany, Europe’s largest economy, came only six days after Secretary of State John Kerry asked his German counterpart, Frank Walter-Steinmeier, to resist the Chinese overtures until the Chinese agreed to a number of conditions about transparency and governing of the new entity. But Germany came to the same conclusion that Britain did: China is such a large export and investment market for it that it cannot afford to stay on the sidelines.

American officials have fumed that China never approached the Group of 7 — the consortium of economic powers that the United States has led — but rather decided to pick off individual members, setting a deadline of the end of March for them to decide whether to join the new organization, the Asian Infrastructure Investment Bank, which many refer to by its initials, the A.I.I.B.