The United States formally offered its backing on Tuesday for French Finance Minister Christine Lagarde to take over the top job at the International Monetary Fund, ensuring a win for her over Mexico's Central Bank Governor Agustin Carstens.

The IMF's 24-strong board meets on Tuesday to go through the formalities of picking a successor to former Managing Director Dominique Strauss-Kahn, who resigned in May to defend himself against charges of sexual assault against a New York hotel maid.

But the 55-year-old Lagarde was set to continue the tradition of having a European head the global lender while also becoming the first woman to lead the IMF.

Geithner nodded to emerging markets' unhappiness at the tradition -- which has a European head the IMF and an American lead its sister institution, the World Bank -- by saying he was pleased that Lagarde had received broad support ... including from emerging countries.

Minister Lagarde's exceptional talent and broad experience will provide invaluable leadership for this indispensable institution at a critical time for the global economy, Geithner said in a statement.

The United States, which holds the most voting power at the IMF, had refused until the final stage of the process to say who it was supporting, although it was widely assumed it would swing its weight behind Lagarde. As late as Monday night, Geithner told reporters he had no interest in announcing our position to you.

In the end, the backing that Carstens garnered from Latin America, Canada and Australia was too thin to break Europe's 64-year hold on the IMF post.

SEARCHING FOR CONSENSUS

IMF board directors, who represent the fund's 187 member countries, want to try to reach a consensus decision on a successor that would let them avoid a formal vote.

The race has been one of the most hotly contested succession battles in IMF history.

In a convention dating back to the creation of the IMF and World Bank after World War Two, Europe has always held the top IMF job, while the World Bank's top post has always gone to an American.

Developing countries have warned against another U.S.-European stitch-up, but some potential candidates from emerging markets decided not to step up because they did not feel they had a fair chance at the job.

Although a long-shot candidate, Carstens vigorously campaigned on his experience as a former IMF official who had first-hand knowledge of developing world economic crises.

Washington holds close to 17 percent of the vote at the IMF, while European nations account for around 40 percent. China and Russia, two of the so-called BRICS emerging market countries, have already said they back Lagarde, with Russia announcing its formal support on Tuesday.

The three other BRIC nations -- India, South Africa and Brazil -- have been quiet on who they support.

Countries such as Egypt, Saudi Arabia, Indonesia, South Korea and French-speaking African nations early on declared their support for Lagarde.

Fears of contagion over an escalating debt crisis in Greece have played in Lagarde's favor over the last several weeks because of her political punch across Europe, IMF board officials said.

A few board directors quietly expressed concern over an unresolved legal investigation into Lagarde's role in a 2008 arbitration payout to a French business. A top French court has put off a decision on the matter until July 8.

One way of dealing with the issue is not to offer Lagarde an IMF contract until the court has made a final decision, a board source suggested.

Assuming Lagarde gets the official nod, she will have to immediately deal with further IMF-EU financing to keep Greece afloat and focus on potentially thorny IMF spillover reports that analyze the economic and policy actions of the world's major economies.

Lingering resentment over the outcome of the latest election process will also require the new managing director to act quickly to reassure developing nations they have a stake in decision-making at the IMF.

(Editing by Paul Simao and Jan Paschal)

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