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.
Strauss-Kahn has been remanded in custody at New York's notorious Riker's 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 Strauss-Kahn, 62, was a flight risk.
He faces seven charges and could be sentenced to up to 25 years in prison.
Strauss-Kahn, who had been seen as a favourite in France's 2012 presidential elections, denies the charges.
The defence offered to post $1 million U.S. bail, with Strauss-Kahn to stay at his daughter's home in New York until the next hearing on Friday. However, Judge Melissa Jackson rejected the application.
The Spanish finance minister 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."
Fekter's comments touched on concerns that, irrespective of the legal outcome, Strauss-Kahn's detention creates a practical obstacle for his role in negotiating rescue loans for Portugal and Greece.
Strauss-Kahn had been due to attend an E.U. finance ministers' meeting in Brussels to discuss financial bailouts.
The IMF has played a central role in organizing 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.
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.
According to the New York Police Department, a 32-year-old maid told officers that when she entered his suite on Saturday afternoon, 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 N.Y.P.D. spokesman added.
Later on Saturday, Strauss-Kahn was detained on board an Air France flight at New York's John F Kennedy airport minutes before takeoff.
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 lineup.
