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Speaking at the European Business Summit, Barroso said it was "only natural that EU countries would feel a responsibility to put forward a good candidate" for the top job at the Washington-based institution.
He admitted that Europe had more than one potential candidate for the post, and said the issue needed to be dealt with soon.
One day before, Jean-Claude Juncker, eurozone president and prime minister of Luxembourg, said that commenting on Strauss-Kahn's successor at this stage was "indecent". Juncker appeared to condemn statements by Germany and Belgium, which have already called for the next IMF chief to come from an EU country.
Asked by EurActiv to comment on Juncker's view, Barroso went on the defensive, saying that he had expressed his opinion in response to a question. German Chancellor Angela Merkel said the same, Barroso added.
Hours later, the IMF released the text of the resignation letter of Strauss-Kahn, in which he denied "with the greatest possible firmness" all allegations made against him.
In the meantime, the battle for the IMF top job gained momentum. The candidacy of France's Economy Minister Christine Lagarde, which was one of the first to be mulled, reportedly received support from Sweden. Dutch Central Bank Governor Nout Wellink suggested outgoing European Central Bank President Jean-Claude Trichet, Bloomberg reported.
South Africa and Russia yesterday said that the next head of the IMF should come from an emerging economy. Trevor Manuel, head of South Africa's National Planning Commission, is "highly respected in the world," Finance Minister Pravin Gordhan said in an interview in Pretoria.
Russian Central Bank Deputy Chairman Sergei Shvetsov said a developing country should be given the chance to run the IMF to better reflect the role of those economies in global trade. South Korea's central bank governor made similar remarks before the announcement late yesterday that Strauss-Kahn would resign.
The Associated Press reported that China's Zhu Min, a special adviser to Strauss-Kahn at the IMF, is one of the potential candidates for the position.
From developing regions, potential candidates also include Turkey's former finance minister and former head of the United Nations Development Programme (UNDP), Kemal Derviş, Singapore's finance chief Tharman Shanmugaratnam, Indian economist Montek Singh Ahluwalia, Mexican Central Bank Governor Agustin Carstens, and former Brazilian Central Bank President Arminio Fraga.