By Tom Pfeiffer
Lagarde is the frontrunner but Bank of Israel Governor and former IMF deputy chief Stanley Fischer said on Saturday he would run, presenting a new challenge to the French minister.
The job has been vacated by Frenchman Dominique Strauss-Kahn, who resigned after his arrest on May 14 on charges of attempting to rape a New York hotel maid.
Lagarde has been on a world tour to drum up support for her bid among emerging market economies. This included a visit on Saturday to the Middle East's economic powerhouse Saudi Arabia.
"I have the honor of having been presented by Bahrain and having the support of other countries (in this region) that have expressed themselves," she said.
After meeting Egypt's finance and foreign ministers, as well as the governor of the Egyptian central bank, she told a news conference the Egyptian government had been "very affirmative" in support of her candidacy.
She is backed by the European Union and a handful of smaller countries from Georgia to Mauritius. Paris is hopeful that Washington and Beijing will also stand behind her.
"If I am elected as director general of the institution, I would have at heart serving all member states, taking account of the diversity of economic development," she said in Cairo.
"I consider I am not the candidate of Europe but I hope to be the candidate of a big consensus of members of the institution."
Asked in Egypt about any possible restructuring of Greek debt, she said: "The goal that must guide us is stability, not something that provokes disturbance and big volatility."
(Reporting by Tom Pfeiffer; Writing by Edmund Blair; Editing by Hans Peters)