The IMF released a letter from the French executive late Wednesday in which he denied the allegations against him but said he felt compelled to resign.
The 62-year-old said he was thinking of his family and that he wanted to protect the IMF.
Strauss-Kahn is on suicide watch at a New York jail, as a lawyer for the alleged victim sought to rebut allegations that the charges were a setup.
Strauss-Kahn is facing a long list of charges including attempted rape and unlawful imprisonment. Authorities say he ambushed a maid who came to clean his suite at the Sofitel hotel and attempted to sexually assault her.
Lawyers for the influential banker claim forensic evidence won't be consistent with a forcible encounter, but the alleged victim's attorney, Jeffrey Shapiro, says that's not possible.
"There is no way in which there is any aspect of this event which could be construed consensual in any manner," Shapiro said. "This is nothing other than a physical, sexual assault by this man on this young woman."
According to Shapiro, the maid came from one of the world's poorest countries to try to support her teen daughter, and to her, the penthouse suite was just another empty room to clean.
Calls had intensified for Strauss-Kahn to step down, with Treasury Secretary Timothy Geithner saying Strauss-Kahn "is obviously not in a position to run" the agency.
Strauss-Kahn was one of France's most high-profile politicians and a potential candidate for president in next year's elections.
"What (Strauss-Kahn) might be able to get away with in some countries, he can't here in this country," Shapiro said.
Strauss-Kahn is expected to appear in court again on Friday. He is being held at Rikers Island.
Norman Seabrook, president of the correction officers union, said Strauss-Kahn did or said something during a mental health evaluation that concerned doctors, and he is being monitored day and night.
The Associated Press contributed to this story.