French prosecutors say Dominique Strauss-Kahn did something to a writer that qualifies as sexual assault, but they can't send him to trial because it happened too long ago and they are dropping the case.

Thursday's announcement is a legal victory, but a moral embarrassment for the suave, assured, and married economist who earlier this year led the International Monetary Fund and was on track to seek the French presidency.

The Paris prosecutor's office said it has dropped an investigation into writer Tristane Banon's claim that he tried to rape her during a 2003 interview for a book the then-23-year-old was writing. But it said _ without offering details _ that Strauss-Kahn admitted during questioning to actions that qualify for the lesser charge of sexual assault.

Strauss-Kahn's lawyer told The Associated Press that the ex-IMF chief admitted only that he tried to kiss Banon without her consent and she refused.

Under French law, sexual assault is an attack that does not involve an attempt to penetrate the victim. Prosecutors can't pursue the charge because the statute of limitations is three years. On attempted rape, it's 10 years.

"For lack of sufficient elements of evidence, prosecution cannot be undertaken on the charge of attempted rape," the prosecutor's office said in a statement. However, it added that "facts that can be qualified as sexual assault have been acknowledged."

The prosecutor's unusual statement revived questions about Strauss-Kahn's behavior toward women that have trailed him throughout his decades in French politics but that remained largely ignored by mainstream French media. In France, politicians' private lives have traditionally been considered off-limits.

Not so in the United States, where Strauss-Kahn was jailed in May on charges he tried to rape a New York hotel maid. Prosecutors later dropped that case, too, but Strauss-Kahn saw his reputation and French presidential ambitions dashed and his personal life exposed.

In the French incident, Banon, a writer 30 years his junior, has said that Strauss-Kahn invited her to an empty apartment for the book interview, and they ended up tussling on the floor, with the politician trying to open her jeans and bra and putting his fingers in her mouth and underwear.

Strauss-Kahn's French lawyer, Henri Leclerc, told The Associated Press that the ex-IMF chief rejected sexual assault.

"He admitted no assault, no violence of any kind," Leclerc said. He said he didn't understand how the prosecutor could have interpreted the attempted kiss as sexual assault.

Strauss-Kahn called Banon's claim imaginary and slanderous, insisting in a televised interview last month that "no act of aggression" had taken place between the two. He did not say anything about an attempted kiss.

Since the police questioning was behind closed doors, it's unclear what exactly what Strauss-Kahn told investigators. And only Strauss-Kahn and Banon know what happened at the February 2003 interview, when he was a respected 53-year-old senior member of France's Socialist Party.

Since Banon filed her complaint in July, legal experts have warned that she would have a tough time proving attempted rape so many years later, and without any material evidence. Banon filed her complaint in France only after doubts about the New York maid's credibility emerged.

Banon's lawyer, David Koubbi, said Strauss-Kahn benefited from an "extremely short statute of limitations."

While "extremely disappointed" that the attempted rape probe was dropped, Koubbi told AP Television News that he's satisified that "the prosecutor recognized in a very clear way that DSK is a sexual assailant."

Koubbi said that other women had told him they were also victims of Strauss-Kahn's sexual behavior but were afraid to testify.

Banon has defended her decision not to file charges against Strauss-Kahn at the time of the alleged incident, when her own mother advised her against lodging a complaint.

In the New York hotel incident, Strauss-Kahn has admitted to what he called an inappropriate sexual encounter with the chambermaid, calling it a "moral failing" that he deeply regrets, but insisting there was no violence.

The maid, Nafissatou Diallo, has filed a civil suit, and Banon has said she may do likewise.

One of Diallo's lawyers, Douglas Wigdor, said the French prosecutors were swayed by the New York prosecutor's decision to drop the U.S. case.

"We have supported and believe that Ms. Banon was sexually assaulted by Mr. Strauss-Kahn and are pleased that the prosecutors in Paris, as has been reported, have found evidence supporting a sexual assault," he said in a statement.

The Associated Press does not generally name accusers in sexual assault cases unless they agree to be named or identify themselves publicly, as Banon and Diallo have done.

French feminists staged a small, quick rally at a Paris courthouse to decry Thursday's decision and urge more attention to sex crimes, which largely go unreported.

"What we are denouncing today is a judiciary system that doesn't work, a judiciary system that denies violence committed against women by men," said Clara Carbunar, member of the French activist group World Women March.

The prosecutor's announcement comes as voters are gearing up for primary elections Sunday to choose the candidate from Strauss-Kahn's Socialist Party for next year's elections. Until May, he had been seen as the party's best hope at unseating conservative President Nicolas Sarkozy.

While Strauss-Kahn, known as DSK here, has not said whether he'll return to politics, his allies welcomed the end of the criminal probe.

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AP video journalist Oleg Cetinic and Associated Press writers Philippe Sotto in Paris and Colleen Long in New York contributed to this report.