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.
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."
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
- 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