In court, Strauss-Kahn's lawyer, Benjamin Brafman, offered to put up $1 million bail.
"We believe and will prove in our judgment that Dominique Strauss-Kahn is innocent of these charges," he said Monday. "We think this case is very defensible."
Brafman has has previously defended Michael Jackson, Jay-Z and football player Plaxico Burress.
Assistant District Attorney John McConnell told reporters the victim provided a "very violent and detailed account" of the assault.
He said she made appeals to multiple witnesses after the alleged attack. She was taken to the hospital for a standard rape examination and the "observations and findings corroborate her account," he said.
The office of Manhattan District Attorney Cyrus Vance Jr. asked that Strauss-Kahn be remanded to jail, a course of action that took shape in the hours after his arrest on Saturday, as the prosecutor's office wrestled with how to balance the rights of the accused with the facts of the case, and his potential to flee their jurisdiction.
In arguing for the remand, McConnell said, prosecutors are obtaining additional information against the suspect, including allegations that he has "engaged in similar conduct at least once before."
"This guy has every reason to run, and the law may even help him hide from this situation," one investigator said.
Strauss-Kahn has had a reputation as "the great seducer" for years. He recently admitted to an affair with a member of the IMF, and French writer Tristane Banon said Monday that she planned to file sexual assault charges stemming from an incident in 2002 when, she said, she had to fight Strauss-Kahn off during an interview for a French television show called "93, Faubourg Saint-Honore."
One woman who stands by his side, however, is his wife, U.S.-born Anne Sinclair. The popular French television journalist said in a statement: "I do not believe for a single second the accusations leveled against my husband."
Strauss-Kahn told a French newspaper last month that his love of women might be his downfall, predicting that a woman would likely falsely accuse him of rape in exchange for a big payoff.
ABC News' Adam Stephan, Lauren Pearle, Michael Murray, Michael S. James and Kevin Dolak contributed to this report.