The candidates now include Jeroen Dijsselbloem, the Dutch former head of euro zone finance ministers; Olli Rehn, the Finnish central bank governor; and Bulgaria's Kristalina Georgieva, the World Bank chief executive.
Nadia Calvino, the Spanish economy minister, quit the race on Friday after a first round of voting among representatives of the EU's 28 nations. Mario Centeno, the Portuguese chairman of euro zone finance ministers, withdrew in Thursday.
Britain opposed the plan to select a candidate now, saying it was "premature" and did not allow London enough time to propose one of its own, according to a confidential note seen by Reuters.
Candidates for the head of the Washington-based IMF can be fielded until Sept. 6. French Finance Minister Bruno Le Maire is leading the process to select a European candidate.
The top job at the world lender has historically been filled by a European, but candidates from elsewhere may gain traction if Europe split.
The former IMF chief, France's Christine Lagarde, resigned in July after EU leaders chose her to replace Mario Draghi as European Central Bank president.
DIVISIONS
Northern European countries prefer Dijsselbloem or Rehn; southern and eastern states are seen pushing for Georgieva, one European official said.
Since an informal compromise was impossible, France decided to push for a vote. A candidate who obtains 55% of the votes of the 28 EU states, representing at least 65% of its population, will win.
The IMF chief should have a proven understanding of how the fund works, a commitment to multilateral organisations and be an effective communicator, the IMF board said. All three European candidates qualify.
Dijsselbloem has steered the euro zone out of the debt crisis, orchestrating with the IMF the bailout of Greece, Cyprus and Spanish banks. But he is opposed by high-debt EU countries for the austerity measures attached to the rescues.
Georgieva, 65, has had a long career at the World Bank, the IMF's twin organisation, but her candidacy would force a change in IMF rules that require the managing director to be less than 65 years old.
Rehn has held top economic jobs at the European Commission and now at the Finnish central bank.
New rounds of voting could be necessary to choose the European candidate.
"It is a mathematical possibility that no-one will make it today," one official involved in the process said. "But I think at the end of the day after a lot of arm-twisting they will come up with one."
Centeno said on Thursday he was pulling out of the race "in this stage of the process", adding he would be available if needed for a compromise solution.
Britain did not field a candidate because it could not come up with a name on time, London said in a note sent to France. A new British government led by Boris Johnson was formed only last week.