Pressure is mounting on Dominique Strauss-Kahn to step down as head of the International Monetary Fund (IMF).
Austrian finance minister Maria Fekter called on him to consider his position.
Meanwhile, her Spanish counterpart, Elana Salgado, gave her support for the victim of his alleged sexual assault.
Mr Strauss-Kahn has been remanded in custody at New York's notorious Rikers Island jail, following his arrest on Saturday for the attempted rape of a hotel maid.
He was arrested after boarding a plane, prompting the judge to say that Mr Strauss-Kahn, 62, was a flight risk.
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He faces seven charges and could be sentenced to up to 25 years in prison.
Mr Strauss-Kahn, who had been seen as a favourite in France's 2012 presidential elections, denies the charges.
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, Judge Melissa Jackson rejected the application.
'Very serious accusations'
"I don't comment on judicial matters," said Ms Fekter. "But in view of the situation, that bail has been refused, he himself must deliberate on whether he is hurting the institution."
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Charges against Dominique Strauss-Kahn
Criminal sexual act in the first degree, two counts (maximum sentence 25 years)
Attempted rape in the first degree, one count (up to 15 years)
Sexual abuse in the first degree, one count (up to seven years)
Unlawful imprisonment in the second degree, one count (up to one year)
Forcible touching, one count (up to one year)
Sexual abuse in the third degree, one count (up to three months)
Source: New York County District Attorney's Office
Spotlight on France's 'macho' political culture
New York DA's news release on charges
The Spanish finance minister added her voice, saying that the IMF head faced "very serious accusations" but that any resignation "is only a decision that Mr Strauss-Kahn can take".
However, she went on to express sympathy for the alleged victim of the assault: "If I had to show my solidarity and support for someone, it would be towards the woman who has been assaulted, if that is really the case that she has been."
In France, meanwhile, leaders from Mr Strauss-Kahn's Socialist party met in Paris and said they objected to the broadcasting of "humiliating" images of the IMF chief in handcuffs.
"I think in a case like this one, there is going to be a victim - Dominique if he is innocent, and of course that's what I wish for," said the party's leader, Martine Aubry.
"I feel extremely painful sentiments. The young woman should be respected, the notion of 'presumed innocent' should be respected."
Irrespective of the legal outcome, though, Mr Strauss-Kahn's detention creates a practical obstacle for his role in negotiating rescue loans for Portugal and Greece.
Mr Strauss-Kahn had been due to attend an EU finance ministers' meeting in Brussels to discuss financial bail-outs.
The IMF has played a central role in organising rescue packages for the troubled economies of Portugal and Greece.
However, according to the Portuguese finance minister, Fernando Teixeira dos Santos, the IMF head's absence had not been an issue.
Mr Strauss-Kahn received support from the Luxembourg prime minister and eurogroup head, Jean-Claude Juncker, a self-professed close friend.
"I'm very sad and upset," he said. "I didn't like the pictures I've seen on television."
French Finance Minister Christine Lagarde described Mr Strauss-Kahn's predicament as "crushing and painful".
Flight halted
The IMF said in a statement that it had been briefed on the charges against its managing director, and that it would "continue to monitor developments".
The charges relate to an alleged assault at the Times Square Sofitel hotel in New York.
Tristane Banon in 2004 Writer Tristane Banon alleges Mr Strauss-Kahn assaulted her in 2002
According to the New York Police Department, a 32-year-old 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.
'Thunderbolt'
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.
Socialist party president Martine Aubry described his arrest as a "thunderbolt" but called for Mr Strauss-Kahn to be presumed innocent.
Mr Strauss-Kahn's wife, French TV personality Anne Sinclair, has also protested his innocence.
Meanwhile, another allegation against Mr Strauss-Kahn has emerged. A French writer says she may file a complaint for an alleged sexual assault in 2002.
Tristane Banon, 31, says Mr Strauss-Kahn tried to rape her when she went to interview him for a book she was writing.
"We're planning to make a complaint," Ms Banon's lawyer told AFP news agency. Mr Strauss-Kahn's lawyers have so far not responded to the allegation.
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