Christine Lagarde, France's minister of finance, speaks to the media following meetings Thursday at the International Monetary Fund in Washington, D.C. (Joshua Roberts/Bloomberg)

Treasury Secretary Timothy Geithner announced Tuesday that the United States was supporting French Finance Minister Christine Lagarde’s bid to become head of the International Monetary Fund, breaking its silence on the controversial decision just as the IMF board prepared to meet.

By throwing its support behind Lagarde, the United States essentially guaranteed that she will become head of the fund, continuing the tradition of having a European in the post but also breaking new ground as the first woman to be chosen.

The United States is responsible for more than 17 percent of the roughly $320 billion kitty that runs the International Monetary Fund, and has by far the largest vote on the fund’s board.

While it usually is not shy about exercising its influence, U.S. officials had maintained a studied silence about who they believed should replace ousted IMF chief Dominique Strauss-Kahn, apparently hesitant to weigh in on a global debate about whether the fund should be led by a banker from a non-European country.

It was not immediately clear why Geithner decided to break that silence at the last minute.

“I am pleased to announce our decision to support Christine Lagarde to head the International Monetary Fund,” Geithner said in a written statement. “Minister Lagarde’s exceptional talent and broad experience will provide invaluable leadership for this indispensable institution at a critical time for the global economy.”

The statement said the United States was “encouraged by the broad support” Lagarde had secured from IMF member countries, “including from the emerging economies.” It commended Mexican central bank governor Agustin Carstens, who is also vying for the job, “on his strong and very credible candidacy.”

The United States was certain to offend important allies no matter who it backed. Side with Lagarde, and the administration becomes part of the old-line European axis — earning the enmity of developing nations and contradicting its own promises of reform. Choose Carstens, and the United States vexes its close allies in Europe, upends that region’s crisis planning, and risks facing opposition to its own traditional prerogatives, such as the choice of a new World Bank president next summer.

Instead, until Tuesday morning, the strategy was to lie low, a stance the Obama administration tried to give a positive spin by saying it was ready to follow the rest of the world rather than play a kingmaker’s role.

Critics, however, argued that neutrality, in this case, is the same as endorsing Lagarde. As a long-shot candidate, and the first credible contender from a developing country, Carstens would have needed a strong push by the United States and other major nations for his candidacy to take hold.

As recently as Monday, a Treasury Department spokesman answered questions about the U.S. position by referring to a five-week-old statement: “We are prepared to support a candidate with the requisite, deep experience and leadership qualities, and who can command broad support among the Fund’s membership.”

The fund’s 24-member board — whose votes are weighted based on the country or coalition of countries they represent — has said it hopes to choose a new managing director by consensus rather than forcing board members to go on record. That method has long-standing roots in an agency that largely has allowed the Western European powers to come up with a candidate that the other nations would accept.

The board said it wants to name a new managing director by Thursday, but the decision could be announced after Tuesday’s meeting.

Carstens’s candidacy added elements of actual competition to the process of choosing a replacement for Strauss-Kahn, who resigned to defend himself against sexual assault charges in New York. Considered by some to be technically superior to Lagarde, given a resume that includes prior ranking jobs at the IMF and his current role running Mexico’s central bank, Carstens has been endorsed by Canada, Australia, Mexico and a handful of Latin American nations.

But that lags behind the announced support for Lagarde, a career lawyer and French cabinet minister who joined the competition for the job with the IMF’s version of a home-court advantage. Several of the executive directors were obligated to her by their heads of state and finance ministers before it was even clear who might compete for the post.

Since then she has won the endorsement of a coalition of African states and of Egypt, the dominant member in a coalition of Arab nations that share a spot on the executive board. Top Chinese and Russian officials also have indicated they support her.