In a challenge to the American-led world financial order, some of the United States’ crucial European allies said on Tuesday that they would join a new development bank for Asia that is largely funded by China and that Washington views as a rival to the World Bank.

The French, German and Italian governments, in a joint statement, announced “their intention to become prospective founding members of the Asian Infrastructure Investment Bank,” known as the A.I.I.B.

The three nations are following the lead of Prime Minister David Cameron’s Conservative-led government in Britain, which last week announced its own decision to join.

The three governments said that the bank, working with existing institutions, “could play an important role to provide funds for addressing the large infrastructure needs in Asia,” and that it would “promote economic and social development in the region and contribute to global growth.”

The bank was initially proposed by President Xi Jinping of China with a mission of helping to fund infrastructure projects in poor Asian countries, something the World Bank and the Asian Development Bank already do. China has pledged a large part of the initial $50 billion of capital, and Beijing hopes the institution will contribute to the expansion of its power base in Asia, even as its growing might, economic and military, reshapes the political dynamics of the region.

Washington had been lobbying against the participation of its allies, fearing that the rise of the Chinese-led lender would erode the institutions, such as the World Bank and the International Monetary Fund, that were created to shepherd the world economy after World War II under American leadership.

In their statement on Tuesday, the three newest European members said they were “keen to work with the A.I.I.B. founding members to establish an institution that follows the best standards and practices in terms of governance, safeguards, debt and procurement policies.”

Before the announcement on Tuesday, the bank had more than 25 members, almost all from developing countries in Asia and the Middle East. Australia, Japan and South Korea have so far refused to join, but the entry of influential European countries could encourage other allies to participate, analysts have said.

When asked to comment on the countries’ statement, Hong Lei, the Chinese Foreign Ministry spokesman, said he welcomed their willingness to become founding members.

“The active participation of countries both inside and outside of the region will make the Asian Infrastructure Investment Bank more broadly representative,” he said.

“China wants to work together with all parties to set up a mutually beneficial, professional infrastructure investment and financing platform to contribute to regional infrastructure and economic development,” Mr. Hong said in Beijing.

While the Chinese economy has grown over the past decades to become the second-largest in the world, after that of the United States, it is still sidelined at the international level by the reluctance of developed nations to relinquish their privileged places. In one case, the United States and its partners at the International Monetary Fund agreed in 2010 to give emerging nations like China an expanded role in the institution. The United States Congress has so far refused to sign on.

Speaking in Washington on Tuesday about the importance of the I.M.F. and the World Bank and of American engagement in those institutions, Treasury Secretary Jacob J. Lew said it was “urgent that we address prior unmet commitments, which have grown to levels that raise significant questions about U.S. credibility and leadership in the multilateral system.”

Failure to do so, he added, could “result in a loss of U.S. shareholding, at a time when new players are challenging U.S. leadership in the multilateral system.”