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Strauss-Kahn was arrested in New York after a maid alleged he had chased her naked down a hotel hallway, sexually assaulted her and tried to lock her in a hotel room.
The charges threatened to create a leadership vacuum at the IMF, overseer of the global economic system, and threw wide open the French presidential election next April, for which opinion polls had made Strauss-Kahn the front-runner.
One of his lawyers, Benjamin Brafman, said his client "will plead not guilty".
The 62-year-old Socialist, a key player in the response to the 2007-9 global financial meltdown and in Europe's debt crisis, was taken off an Air France plane about to leave for Paris from John F Kennedy International Airport on Saturday.
New York police spokesman Paul Browne said he was charged with a criminal sexual act, unlawful imprisonment and attempted rape. He is expected to go before a state court later on Sunday.
The arrest caused shock and disbelief in France, where a government spokesman called for caution and respect for the presumption of innocence.
"The news we received from New York last night struck like a thunderbolt," said Socialist leader Martine Aubry, appealing for party unity.
Francois Bayrou, a centrist opponent of Strauss-Kahn, said: "All this is completely astounding, immensely troubling and distressing. If the facts prove true [...] it's something degrading for all women. It's terrible for the image of France."
Far-right leader Marine Le Pen said her rival's presidential hopes had been crushed. Strauss-Kahn and Le Pen have led recent opinion polls ahead of conservative President Nicolas Sarkozy, even though the chief of the International Monetary Fund had yet to declare his candidacy.
In a statement on its website, the Fund declined to comment on the case, saying only that it "remains fully functioning and operational".
But a Greek official told Reuters the arrest could cause some short-term delays in discussions over a European Union/IMF bailout for Athens, in which Strauss-Kahn was closely involved, by forcing the cancellation of key meetings.
Strauss-Kahn had been scheduled to meet German Chancellor Angela Merkel on Sunday and attend a meeting of eurozone finance ministers the following day to discuss the eurozone debt crisis and how to handle Greece's difficulties in meeting bailout targets and regaining market trust.
"The Greek government continues, without interruption, its programme to get out of the crisis," government spokesman George Petalotis said in a statement.
Strauss-Kahn's wife Anne Sinclair said in a statement: "I do not believe for a single second the accusations levelled against my husband."
She added: "I do not doubt his innocence will be established. I appeal for restraint and decency."
One of the IMF chief's French-based lawyers, Leon Lef Forster, said: "We must wait until things settle and see if it's true or a provocation. We must be especially careful not to get into a media circus."
A 32-year-old maid filed a sexual assault complaint after fleeing the $3,000-a-night hotel suite at the Sofitel in Times Square where the alleged incident occurred around 1 p.m. (1700 GMT) on Saturday, Browne said.
Strauss-Kahn appeared to have fled the hotel after the incident, the police spokesman said.
Browne said: "She told detectives he came out of the bathroom naked, ran down a hallway to the foyer where she was, pulled her into a bedroom and began to sexually assault her, according to her account.
"She pulled away from him and he dragged her down a hallway into the bathroom where he engaged in a criminal sexual act, according to her account to detectives. He tried to lock her into the hotel room."
Strauss-Kahn does not have diplomatic immunity, Browne said.
According to New York state law, a criminal sexual act carries a potential sentence of 15-20 years, the same as attempted rape. Unlawful imprisonment carries a potential sentence of three to five years.
The allegation is a major embarrassment to the IMF, which has authorised billions of dollars of lending to troubled countries and played a major role in the euro zone debt crisis.
France in shock
Popularly known by his initials DSK, the IMF managing director had been expected to declare by late June if he would run for president of France. The latest opinion polls ranked him as a clear winner over conservative incumbent Sarkozy.
"The case and the charges [...] mark the end of his campaign and pre-campaign for the presidency and will most likely prompt the IMF to ask him to leave his post," National Front leader Le Pen told i-Tele television.
Conservative Trade Minister Pierre Lellouche said: "I think we have to grant DSK the presumption of innocence. If all this were true it would be damning."
Even Strauss-Kahn's political allies were pessimistic.
"The most likely outcome is that this case will stick and even if he pleads not guilty, which he may be, he won't be able to be candidate for the Socialist primary for the presidency and he won't be able to stay at the IMF," said prominent Socialist Jacques Attali.
If Strauss-Kahn were out of the race, leading candidates for the Socialist presidential ticket include party leader Aubry, left-wing veteran Francois Hollande and Segolene Royal, the candidate beaten by Sarkozy in 2007.
Europe's influence on the IMF diminished
Strauss-Kanh's arrest follows a Thursday statement that the IMF's No. 2, John Lipsky, plans to step down in August when his term ends.
A crisis of leadership at the Fund would especially worry European nations, given Strauss-Kahn's pivotal role in brokering bailouts for Iceland, Hungary, Greece, Ireland and Portugal.
Strauss-Kahn's arrest may also bolster a drive by Brazil and other emerging markets for a greater voice in the selection of the IMF and World Bank chiefs, Bloomberg reports.
"The chances are the successor won't be a European, and will want to rebalance the IMF's priorities away from its massive commitment in Europe," said Jean Pisani-Ferry, director of the Bruegel economic think-tank.
"This event is likely to put into play the leadership and governance structure of the IMF in a dramatic and unanticipated manner," said Eswar Prasad, a senior fellow at the Brookings Institution in Washington and a former IMF official. He told Bloomberg it was "untenable" for Strauss-Kahn to keep his job, and that Europeans may be unable to make a strong case to maintain control of the post.
Since taking over the IMF, the Frenchman has won praise for putting it at the centre of efforts to tackle the global financial meltdown. He introduced sweeping changes to ensure countries swamped by the crisis had access to emergency loans.
He has overseen changes that have given emerging market countries, such as China, India and Brazil, greater voting power in the IMF, and weighed into thornier issues by urging China to let its currency rise in a dispute with the United States.
(EurActiv with Reuters.)