Assistant District Attorney John McConnell told reporters today 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 District Attorney Cyrus Vance Jr. asked that Strauss-Kahn be remanded to jail, a course of action that took shape in the hours after the IMF chief's arrest 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.
He has personal, political and financial resources to evade capture, the DA's office said in open court. He is, an assistant district attorney said, an "incurable" flight risk.
His defense team -- Ben Brafman and William Taylor, among the best criminal defense attorneys money can buy -- spent hours behind the scenes attempting to structure terms that would have allowed their client to stay out of jail while defending himself against the charges.
In court today, Brafman argued that Strauss-Kahn had a "very important" incentive to clear his name.
Strauss-Kahn is "entitled to bail" and prepared to stay with his daughter at her New York City apartment, the lawyer said. Strauss-Kahn also offered to post $1 million bail.
Brafman called his client the "most easily identifiable person in the world" right now and he called the case against him "very defensible."
He added that it was inaccurate to suggest that Strauss-Kahn rushed to the airport. Brafman said his client had been at a several hours-long lunch appointment between the time of the alleged incident and when police caught up with him aboard an Air France plane at Kennedy Airport scheduled to depart for Paris.
Like Strauss-Kahn, most of the Rikers Island complex inmates are in pretrial status -- awaiting trial. Most of those are in dorms housing 50 to 60 inmates in a self-contained unit with a day room, television, a shower and other facilities, according to New York's Department of Corrections.
Strauss-Kahn will be locked in his cell after lights out, the department said. He will eat his meals in his cell, standard practice for inmates housed in a cell, and be allowed out for an hour a day for outdoor exercise. He also will be able to walk in the corridors and areas adjacent to his cell from time to time during the day. He can leave for visitors and he can leave for the commissary.
Strauss-Kahn will not have proximity or contact with other inmates. Each time he is authorized to leave his cell he will be accompanied by corrections officers.
Strauss-Kahn, until this weekend, oversaw the International Monetary Fund, a body established to keep the global monetary system stable, with the ability to lend hundreds of billions of dollars.
He was considered a legitimate contender for the French presidency in an upcoming election, and his arrest has reportedly sparked "shock and disbelief" in France.
ABC News' Adam Stephan, Lauren Pearle, Michael Murray and Michael S. James contributed to this report.