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.
'Honest woman'
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.
The lawyer for Mr Strauss-Kahn's alleged victim says his client, a 32-year-old hotel maid, is living through an "extraordinary" trauma and is now in hiding.
"It's not just my opinion that this woman is honest," Jeffrey Shapiro said. "The New York City Police Department (NYPD) reached the same conclusion. This is a woman with no agenda."
"Start Quote
It's not just my opinion that this woman is honest. The New York City Police Department reached the same conclusion"
Jeffrey Shapiro Accuser's lawyer
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.
Mr Geithner refused to be drawn on the legal challenges facing Mr Strauss-Kahn
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 Maria Fekter said Mr Strauss-Kahn was "hurting" the organisation.
West African immigrant
More details have been emerging about the woman who accused Mr Strauss-Kahn of assaulting her in the suite at the Sofitel hotel near Times Square.
Jeffrey Shapiro 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 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."
Mr Shapiro also said that his client only became aware of who Mr Strauss-Kahn was after the police were called.
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.

BBC