Dominique Strauss-Kahn is "not in a position to run" the International Monetary Fund after his arrest over an alleged sexual assault, US Treasury Secretary Timothy Geithner has said. Mr Geithner said the IMF's executive board should designate an interim head. The alleged assault on a maid happened at New York's luxury Sofitel hotel on 14 May. Mr Strauss-Kahn - who denies the claims - has been put on suicide watch in the city's infamous Rikers Island prison. As a precaution, guards are required to check on him every 15 to 30 minutes. The 62-year-old, who had been seen as a favourite in France's 2012 presidential elections, faces seven charges and could be sentenced to up to 25 years in jail. The defence offered to post $1m (£617,000) bail, with Mr Strauss-Kahn to stay at his daughter's address in New York until the next hearing on Friday. However, a New York judge rejected the application. Mounting pressure Addressing the Harvard Club in New York on Tuesday, Mr Geithner said the most important thing for the IMF was that it found a leader to fill Mr Strauss-Kahn's shoes. "He is obviously not in a position to run the IMF," Mr Geithner said. "It is important that the board of the IMF formally put in place for an interim period someone to act as managing director." It is the first time that a top official from President Barack Obama's administration has publicly spoken about the impact of Mr Strauss-Kahn's alleged sexual assault. However, Mr Geithner refused to comment on the case or the details of the charges against Mr Strauss-Kahn. Since Mr Strauss-Kahn's arrest last Saturday, his deputy John Lipsky has been serving as acting managing director of the global lending agency. Washington has a major say in determining who runs the IMF, because it has the largest number of votes in the organisation. Mr Strauss-Kahn is not due back in court until Friday - and there are growing calls for the IMF to fill the leadership vacuum, the BBC's Steve Kingstone in Washington reports. Earlier, Austrian Finance Minister said Mr Strauss-Kahn was "hurting" the organisation. 'Honest woman' Meanwhile, more details have emerged about Mr Strauss-Kahn's alleged victim. One of her lawyer said she was currently living through an "extraordinary" trauma. Jeffrey Shapiro said the 32-year hotel maid - who has not been named - was now in hiding and felt "alone in the world". He said she was an immigrant from the West African nation of Guinea. She arrived in the US seven years ago and was living with her teenage daughter. Mr Shapiro said her story of being assaulted by Mr Strauss-Kahn in the hotel suite near Times Square was "consistent" because she was telling the truth. "There is no way in which there is any aspect of this event which could be construed consensual in any manner. This is nothing other than a physical, sexual assault by this man on this young woman." The lawyer added: "It's not just my opinion that this woman is honest. The New York City Police Department (NYPD) reached the same conclusion. This is a woman with no agenda." Mr Shapiro also said that his client only became aware of who Mr Strauss-Kahn was after the police were called. Formal identification The charges relate to an alleged assault at the Sofitel hotel, which is located in the heart of New York. According to the NYPD, the maid told officers that when she entered his suite on Saturday afternoon, Mr Strauss-Kahn emerged from the bathroom naked, chased her and sexually assaulted her. The woman was able to break free and alert the authorities, a NYPD spokesman added. Later on Saturday, Mr Strauss-Kahn was detained on board an Air France flight at New York's John F Kennedy airport minutes before take-off. The IMF chief underwent medical examinations on Sunday. Police were looking for scratches or any other evidence of his alleged assault. He was later charged with a "criminal sexual act, unlawful imprisonment and attempted rape". Police say the maid formally identified him in a line-up. Until he was arrested, Mr Strauss-Kahn was considered a favourite to become the Socialist candidate for the French presidency next year. Opinion polls gave him a good chance of defeating President Nicolas Sarkozy. Mr Strauss-Kahn's wife, French TV personality Anne Sinclair, has also protested his innocence. Meanwhile, another allegation against Mr Strauss-Kahn has emerged. French writer Tristane Banon, 31, says she may file a complaint for an alleged sexual assault in 2002. Source: BBC