French Finance Minister Christine Lagarde, who is emerging as Europe’s favorite to replace Dominque Strauss-Kahn as head of the International Monetary Fund, would enter any contest for the position with as many as a third of the votes on the agency’s board already locked up.

The prospect that Lagarde could be all but anointed before the competition even begins is casting doubt on whether it will be an open process, as the board has promised. This is putting the Obama administration in a sensitive position as the arbiter between Europe and developing nations, which are eager to see one of their own in the top post.

Regional loyalties are shaping a debate that the fund’s executive board has announced as “open, merit-based and transparent.” Major European powers including Germany and Britain have already committed to Lagarde — without knowing the full list of candidates. Asian and Latin American nations are lobbying for their own local favorites, including Agustin Carstens, head of the Mexican central bank and a former deputy managing director of the IMF.

Underscoring European arguments that Europe must remain the IMF’s immediate focus were the decisions by credit rating agencies Monday to downgrade the outlook for government debt issues by Italy and Belgium, which are trying to avoid the financial crisis of several neighbors. Italy’s rating outlook was cut by Standard and Poor’s, while Fitch Ratings downgraded the outlook for Belgian debt, pointing to the toll that country’s political deadlock is taking. A scramble by Greece, already rocked by a debt crisis, to sell off public property further underlined Europe’s troubles.

Over the weekend, Spain’s incumbent socialist party lost in elections, adding to concern that the budget cuts, tax increases and other measures urged by the IMF are starting to wear at the social fabric in the continent’s more heavily indebted countries.

Strauss-Kahn had been forceful in pushing Europe to address its problems. The French economist resigned after being charged in an alleged sexual assault in New York.

Mexico’s announcement that it will nominate Carstens means the fund’s 24-member executive board will for the first time have a non-European candidate — and face the possibility of a divided vote for a position that has for 60 years been filled by a genteel, Eurocentric consensus.

Carstens on Monday sent the fund’s governing board a letter detailing his qualifications, including his involvement in resolving Mexico’s financial crisis in the 1980s and later work at the top levels of the IMF. Noting the fund’s “spirit of cooperation,” he told the board that a truly open selection for its leadership “is essential for the Fund’s legitimacy, cohesion, and effectiveness.”

Singapore Finance Minister Tharman Shanmugaratnam has won public endorsements from some in Asia. However, he recently took on additional responsibility as deputy prime minister and head of Singapore’s Monetary Authority — equivalent of a central bank — and is not considered likely to pursue the IMF post.

U.S. officials have hoped that the selection process will reflect the sensitivity among developing nations over Europe’s hold on the IMF’s executive suite, which dates from the agency’s founding focus on the continent’s economic recovery after World War II.

The board structure still leans toward Europe. Eight European board members control more than 34 percent of the IMF voting shares. Countries such as China, by comparison, have a vote far less than their share of world economic activity — the result of a complicated formula that reflects statistical measures and political negotiation.

The process announced Friday gives national officials and IMF executive directors until June 3 to nominate candidates, with a short list of three to be interviewed and a final decision expected before July 1.

Although the IMF board outlined a process in which nominations were intended to be made in confidence, the public rush to support Lagarde has given some outside analysts pause.

Referring to the gathering momentum for Lagarde as a “sordid backroom deal among yesterday’s powers,” a coalition of advocacy groups including anti-hunger group Oxfam and the Bretton Woods Project, an IMF and World Bank monitoring group, urged the fund to select the next director by a majority vote of its 187 members. The current system gives greater voting weight to the nations that contribute the most to the IMF’s operations.

The pivotal decision under the current system will rest with the Obama administration. The United States has a 16 percent voting share — enough, combined with the European votes, to put Lagarde in office, or given the likely U.S. sway over other nations, to press for the first non-European.

U.S. officials have not committed, and say they remain open to all candidates.

But to back a non-European candidate would mean pressure to open the competition for World Bank president when Robert Zoellick’s term ends next year. That is something the administration has not promised to do, and it is complicated by domestic politics: a Republican controlled Congress may be hesitant to approve a large contribution to the bank while giving up the United States’ ability to appoint its head.

Lagarde is well-regarded within the administration and well-known in the United States. She worked at the Chicago-based Baker & McKenzie law firm for more than 20 years, including five years as its chairman. She was a main broker of the deal last year that persuaded Germany to help underwrite the debts of other European countries and helped avoid what may have been a series of devastating government defaults.

Lagarde has not yet confirmed she is a candidate, and would have to confer with French President Nicolas Sarkozy about leaving his cabinet ahead of what is expected to be a tough reelection campaign.

But if she pursues the post, she may be tough to beat.

It may be hard as well for emerging markets to combine behind as single candidate. Even Mexico’s representative on the governing board may face conflict. Like most members of the board, Carlos Perez-Verdia represents a consortium of IMF members. His group includes Spain, which, as a European country facing its own debt issues, may argue for Lagarde.

Nancy Birdsall, president of the Center for Global Development, is among those pushing for more open competition at the IMF, but acknowledged that for jobs such as IMF managing director there would be many equally qualified candidates from around the world, likely sharing similar views on policy. It would be difficult to argue that one is better than the other, and difficult as well to strip Europe of its prerogative without looking at similar deals cut for other regions and countries at places such as the World Bank and the Asian Development Bank.

“This is not about fundamental issues,” she said. “It is about short-term narrow political patronage.”