In a statement released Thursday, Sarkozy called Strauss-Kahn's resignation "inevitable" and called for an "open and transparent selection process" for Strauss-Kahn's replacement.
CNN: Ex-IMF chief granted bail amid sexual assault allegations
Strauss Kahn's statement also said the women's testimony had been disclosed at an "opportune time, " just before the final round of the French presidential election.
Meanwhile, the head of the International Monetary Fund, Dominique Strauss Kahn, told the BBC that the most important thing was for countries to clean up their balance sheets.
Under Mr. Strauss-Kahn, the IMF promoted multiple European bailouts and we doubt that will change.
Mr Strauss-Kahn abandoned plans to run after he was accused of rape last year.
Many euro-zone governments hoped Mr. Strauss-Kahn could find a way to relax the IMF's summer deadline.
WSJ: European Disunion: Dithering at the Top Turned EU Crisis to Global Threat
In a statement issued by his attorneys to Agence France Presse, Strauss-Kahn denied the allegations.
Ms Lagarde replaced its disgraced former chief Dominique Strauss-Kahn less than two years ago.
Both Mr Fabius and Mr Strauss-Kahn sent messages of congratulation soon after their defeat.
ECONOMIST: S��gol��ne Royal ushers in a new era of French politics
Some, such as Mr Strauss-Kahn, are less interventionist than others, such as Ms Aubry.
The two women told French press that the Strauss-Kahn case had inspired them to come forward.
Every couple of months Mr Strauss-Kahn drops into Paris, lunching and dining with the right people.
Ms Royal has her eye on the presidency, as does Dominique Strauss-Kahn, boss of the IMF.
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Yet Mr Hollande's score is shared with Mr Strauss-Kahn and a handful of others.
Mr Strauss-Kahn's twin search for legitimacy and relevance will soon be put to the test.
Mr Strauss-Kahn's predecessor, Rodrigo de Rato, left the post after only three years, for personal reasons.
More important in the short term is the political fall-out from Mr Strauss-Kahn's departure.
There is, however, a different reason to be worried about the loss of Mr Strauss-Kahn.
Mr Jospin has already lost a clever finance minister, Dominique Strauss-Kahn, to allegations of corruption.
The IMF chief, Dominique Strauss-Kahn, has suggested the crisis is not over until job growth returns.
"L'Affaire Cahuzac" has struck French consciences as deeply as Dominique Strauss-Kahn's sex scandal in 2011.
Strauss-Kahn, like other avatars of the system, reveled in his own kind of aristocratic and exclusive playground.
CNN: Can France handle truth on sex lives of rich and powerful?
Yet IMF head Dominique Strauss-Kahn is no fan of introducing a so-called "Tobin Tax" on financial transactions.
Mr Strauss-Kahn's easy charm may not be enough to keep them happy when the euro-11 gets going.
We do know that Depardieu has agreed to play the leading role in a film about Dominique Strauss-Kahn.
Mr Sarkozy's UMP party has previously denied any allegations it was involved in a plot against Mr Strauss-Kahn.
Mr Strauss-Kahn had arranged for a friend to examine the phone upon his planned arrival back in Paris.
Ms Banon's lawyer, David Koubbi, said this week that she was intending to press charges against Mr Strauss-Kahn.
For Mr Strauss-Kahn, it is awkward to be yoked to a policy platform so far to his left.
The New York arrest of IMF chief Dominque Strauss-Kahn on sex assault charges is explored in most papers.
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