FRANKFURT — The long-shot bid by Stanley Fischer, the governor of the Bank of Israel, to become managing director of the International Monetary Fund appeared to already be over after the international lender’s executive board said late Monday that it would only consider two other candidates.

The board said in a statement that it would consider the candidacies of Christine Lagarde, the finance minister of France who is seen as the front-runner, and Agustín G. Carstens, the governor of the Mexican central bank.

Without mentioning Mr. Fischer by name, the board statement suggested that he had missed the deadline for submitting his application. “The period for submitting nominations for the position of the next managing director closed on Friday, June 10,” the board said.

Mr. Fischer, a former deputy director of the I.M.F. and influential economist, announced his candidacy on Saturday.

However, Mr. Fischer said that he had been eliminated because, at 67, he exceeds the age limit of 65 for candidates for managing director.

He criticized the I.M.F. for refusing to change its rules.

“I think that the age restriction, which was set in the past at 65, is not relevant today,” Mr. Fischer said in a statement Tuesday. “I was hoping that the I.M.F. board of directors would change its regulations, not only for the sake of my candidacy, but also for the sake of future candidates for the position of managing director.

“I have no regrets for having submitted my candidacy,” Mr. Fischer said.

He said he would remain as governor of the Bank of Israel.

A former vice chairman of Citigroup who is credited with stabilizing the Israeli currency and steering the country through the global financial crisis, Mr. Fischer probably would have also faced opposition from Arab countries. He is a citizen of the United States and Israel.

The I.M.F. board’s decision seems to clear the way for Ms. Lagarde to assume the post, which became vacant after Dominique Strauss-Kahn resigned last month to fight charges he sexually assaulted a hotel maid in New York.

Ms. Lagarde has been on a worldwide tour of countries including Brazil, India and China in what appears to be a successful campaign to win support from developing nations.

Russia has also nominated Grigori A. Martchenko, Kazakhstan’s central bank president. He also appeared to have been ruled out by the I.M.F. board.

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