By Asma Alsharif
French Finance Minister Lagarde is the frontrunner for the job left vacant by the resignation of compatriot Dominique Strauss-Kahn, but she is working hard to persuade emerging powers angry that another European is being appointed.
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"Saudi Arabia plays an important role in the world economy and so we will call for strengthening the kingdom's role and share in the IMF," Ibrahim Alassaf told reporters in Jeddah after the pair met.
He also called for an increase in the number of Saudis working in leadership roles in the IMF.
The kingdom has a 2.81 percent share in the fund, according to the IMF website. This compares with the U.S. which has the largest share of 16.78 percent.
Lagarde is backed by the European Union and a handful of smaller countries from Georgia to Mauritius and is hoping for support from China and the United States that would all but guarantee her the job.
South Africa's Trevor Manuel ruled himself out of the race for the job on Friday, making Lagarde an even firmer favorite, although she remains under threat of a judicial inquiry in her home country.
Her main remaining international competition is from Mexican central bank chief Agustin Carstens.
Lagarde said she would make tackling sovereign debt troubles a priority for the IMF if appointed.
"There are specific issues to deal with and clearly some of the sovereign debt crisis issues are one of the priorities at the moment," Lagarde told Reuters earlier on Saturday.
"I will certainly look at one of the purposes of the fund which is to restore stability."
Lagarde said that the IMF should also support countries affected by the pro-democracy protest movement sweeping North Africa and the Middle East.
"If I were elected I want to participate as closely as possible, bringing the special expertise of the fund in order to help out those countries together with the bilateral support that is given by specific countries such as Saudi Arabia," she said.
Riyadh has pledged $4 billion in aid to Egypt and was also instrumental in a $20 billion handout to Bahrain and Oman for job-creating projects.
One potential pitfall for Lagarde is a legal investigation into her role in a 2008 arbitration payout to a French businessman.
A top French court on Friday put off until July 8 its decision on whether to open a formal inquiry into allegations by opposition left-wing deputies that she abused her authority in approving a 285 million-euro payout to a businessman friend of President Nicolas Sarkozy.
(Reporting by Asma Alsharif; Writing by Jason Benham; Editing by Brian Love and Patrick Graham)