The post of managing director of the International Monetary Fund -- which by convention but not rule goes to a European -- became available after Christine Lagarde was tapped to lead the European Central Bank.
French Finance Minister Bruno Le Maire, who is leading the effort to find common ground on the EU's pick to head the Washington-based global lender, had opted to hold the vote after EU states failed to find a consensus on a single candidate.
They had been discussing an informal shortlist of half a dozen candidates but this narrowed to three Friday as two contenders from southern Europe bowed out of the race.
Portuguese Finance Minister Mario Centeno dropped out and was followed by Spain's Economy Minister Nadia Calvino.
The Spanish government indicated it had withdrawn her candidacy in the name of European unity, saying Madrid supported a "consensus" around a single candidate.
Britain declined a last minute invitation to field a candidate, the French finance ministry said, after rumours said that Canadian-born Bank of England governor Mark Carney could be interested.
- Bulgarian favourite -
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This leaves three contenders: former Dutch finance minister Jeroen Dijsselbloem, Bank of Finland chief Olli Rehn, and the World Bank's second-in-command Kristalina Georgieva of Bulgaria.
But there has been no consensus on a candidate, reflecting deep divisions in the European Union over the IMF's role during the financial crisis.
Nations in southern Europe have long memories of the tough austerity measures imposed as part of the IMF-backed debt bailouts, which they say choked off the economic growth they badly needed to recover.
Southern countries chafe at the prospect of a Dijsselbloem candidacy because of his tough stance against nations like Greece when he headed the group of EU finance ministers.
"I can't spend all my money on drinks and women and then ask for help," he said in one particularly notorious comment in 2017.
A source close to the discussions, asking not to be named, said the candidate currently garnering the most support is Georgieva, who has served as chief executive of the World Bank since 2017.
However she will be 66 later this month and this would infringe the rule that the managing director must be under 65 when appointed. Other fund members would have to make an exception for her "which is not a given", according to a source.
- 'Several rounds of voting' -
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The vote is being held under the EU's qualified majority voting rules and the winner will need the backing of at least 16 of the bloc's 27 member states, representing at least 65 percent of its population.
"Several rounds of voting will be organised if necessary," the French finance ministry said.
The IMF plans to select its new leader by October 4. Since its creation in 1944, the fund has always been led by a European, while by convention a US citizen is in charge of the World Bank.
The convention has come under strain in recent years, with developing economies demanding a greater say at the Washington-based institutions.
US Treasury Secretary Steven Mnuchin emphasised at a meeting of G7 ministers last month that naming a European to head the IMF was a convention, "not an official policy".
Possible non-European candidates could include the general manager of the Bank of International Settlements and former Bank of Mexico governor Agustin Carstens, and Lesetja Kganyago, the governor of the central bank of South Africa.