Dominique Strauss-Kahn, the managing director of the International Monetary Fund, who is facing attempted rape charges in New York, announced his resignation late Wednesday night.

In a statement, Strauss-Kahn said he is resigning “with infinite sadness” in an effort “to protect this institution.”

The resignation, while providing clarity to an organization reeling from the accusations facing its managing director, immediately sets off a scramble about who will lead the powerful organization and what that will mean for the global economy.

Under Strauss-Kahn, the Washington-based IMF has taken a muscular approach toward fixing Europe’s financial woes, advocating financial bailouts for ailing nations such as Greece and Portugal. Without Strauss-Kahn at the helm, Europe is at risk of losing a key source of financial support in its efforts to contain the debt crisis buffeting the continent.

The resignation — emanating from a jail cell on Riker’s Island, where Strauss-Kahn has spent three nights while he fights to be released on bail — also marks one of the most extraordinary falls from power in recent years. Until the recent accusations, Strauss-Kahn was considered a leading contender to challenge French president Nicholas Sarkozy in next year’s election.

The resignation comes four days after Strauss-Kahn was removed from a Paris-bound plane in New York and arrested on charges of attempted rape. He is accused of sexually assaulting a housekeeper at the lavish Sofitel hotel in Midtown Manhattan.

His departure from the fund came after he faced pressure to resign from Treasury Secretary Timothy F. Geithner and other economic officials around the world.

John Lipsky, an American banker who serves as the first deputy managing director at the IMF, is temporarily overseeing the organization until it finds a new managing director.

In his letter — his first statement since the allegations — Strauss-Kahn wrote that he denies “with the greatest possible firmness all of the allegations that have been made against me” and wants to devote his time “to proving my innocence.”

The news of Strauss-Kahn’s resignation comes after his offer Wednesday to submit to electronic monitoring of his movements and 24-hour-a-day house arrest at his daughter’s apartment in New York in an effort to end his confinement at Rikers Island jail while awaiting trial. In addition to offering a $1 million cash bail, the embattled IMF chief proposed the electronic monitoring and “home detention” in a plea for release filed by his attorneys in New York Supreme Court on Wednesday.

A hearing has been set for Thursday afternoon, and in a statement Strauss-Kahn’s attorneys said they were confident their high-profile client would be released.

The documents filed with the court “proposed conditions that should satisfy any concerns about Mr. Strauss-Kahn’s leaving the city. . . . We hope to have him released from Rikers Island promptly,” lawyers William W. Taylor III and Benjamin Brafman said in a statement.

In an initial bail hearing after Strauss-Kahn’s Saturday arrest, New York prosecutors maintained that his wealth and prominence made him a flight risk. The judge agreed, noting that he was taken off an Air France plane waiting to leave for Europe when he was arrested.

The IMF chief and onetime prospective candidate for the French presidency also has surrendered his French passport and diplomatic travel documents and promised in a signed affidavit “to voluntarily appear . . . for all proceedings relating to the matters for which I am charged.”

As his attorneys worked for his release from the notorious New York holding facility, investigators pressed the hunt for forensic evidence to back up the claims of a hotel maid who alleges that a naked Strauss-Kahn attacked her as she tried to clean his suite at the Sofitel in Manhattan.

The Associated Press, quoting anonymous law enforcement officials in New York, said investigators had removed a section of carpet from the room to see whether it contained evidence of bodily fluids that could corroborate the hotel worker’s account of forced oral sex with Strauss-Kahn.

A New York grand jury was considering the case this week, including potential testimony from the maid. The woman, a native of Guinea, is “prepared to do whatever she is asked to do” to pursue the case, her attorney, Jeffrey Shapiro, said in televised and other interviews Wednesday.

Strauss-Kahn’s attorneys have said he plans to plead not guilty to the seven criminal counts lodged against him, which carry a possible prison term in excess of 25 years. Along with the bail hearing Thursday, Strauss-Kahn is expected in court Friday, when a grand jury is scheduled to decide whether to indict him.

On Tuesday, Geithner had said Strauss-Kahn’s legal problems meant he could not effectively run the organization he had been guiding for four years.

Even before Strauss-Kahn’s resignation, the fight to choose a successor had begun to lay bare the tension within the agency between the developed nations that still largely pay its bills and the developing countries such as China, India and Brazil that are reshaping the global economy.

For at least a decade, the IMF has discussed ending Europe’s traditional hold on the top job, and two years ago the Group of 20 economic powers — including the United States and major European nations — agreed that the IMF head “should be appointed through an open, transparent and merit-based process.”

A growing group of nations and outside analysts argue that Strauss-Kahn’s departure would be the time to make good on that promise. “There has been a clear understanding repeated in communique after communique that the time has come to change past practice” that allowed Europe to nominate a candidate that the other nations accepted, said Amar Bhattacharya, director of the Group of 24, an organization based inside the IMF that coordinates policy among developing nations. “There are very, very strong, able candidates from the developing world.”

Such a choice would partly be a matter of prestige and standing — a recognition that developing nations are beginning to drive world economic growth, account for a larger portion of its economic output and have developed a strong pool of financial talent.

But it is also about the nature of the IMF and the policies it pursues. Strauss-Kahn had shown the importance of having the right person in the job, earning credit for using his deep connections as a leading French politician to persuade other European leaders to confront a burgeoning debt crisis.

His performance, in fact, had been used as an argument for leaving the job with a European; the continent that poses some of the more difficult problems facing the global economy, it is argued, needs one of its own at the helm of the IMF.

But “for most of the history of the IMF, given the identity of the borrowers, should the head have come from the developing world?” Nicolas Veron and Arvind Subramanian, analysts at the Peterson Institute for International Economics, asked in an essay arguing that it was time to open the competition for the next IMF chief. During the Asian financial crisis in the 1990s, they wrote, there was no suggestion that an Asian should have headed the organization as it imposed strict conditions on countries such as Indonesia.

Under the fund’s governing articles, the executive board has authority to hire — and fire — the managing director virtually at will. The job can be filled by a simple majority vote, and any managing director “shall cease to hold office when the Executive Board so decides.”

But the IMF’s governing structure will not make it easy to change the traditional procedure for selecting a managing director, particularly if the United States and at least some European nations do not go along.

The 24-member executive board is designed to represent the fund’s 187 members, but voting power on the body is weighted based on each country’s financial contribution to the IMF.

In practice, that means the United States and eight European directors hold among them a voting majority; including other developed nations such as Japan, Canada and Australia, the total approaches 65 percent.

Developing countries have about 35 percent of the voting power on the board. Larger nations such as India and China have their owns seats, while other countries are grouped into constituencies.