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Lagarde, who has undertaken a massive campaign and who has the backing of Europe and the US appeared to be odds-on favourite for the new managing director which is to be announced by June 30.
"The Executive Board will meet with the candidates in Washington and, thereafter, meet to discuss the strengths of the candidates and make a selection," the official IMF statement said.
The two were the only ones named when the IMF released the list after nominations closed Friday. The IMF did not explain why Fischer, who only declared himself at the last minute, was not on the list.
Two other possibles, a South African minister and Kazakhstan`s central bank head, dropped out Friday.
While Lagarde, a French national, is Minister of Economy, Industry and Employment of France; Carstens is Governor of the Bank of Mexico. Carstens, 53, has also spent three years as IMF second deputy managing director from 2003-2006.
Both have crisscrossed the globe seeking endorsements from the major economies, but only Lagarde, 55, has picked up major support, foremost from the powerful European bloc.
The IMF`s top post fell vacant unexpectedly after Frenchman Dominique Strauss-Kahn resigned on May 18 to fight sexual assault charges in New York.
