Testing their new clout in the world economy, developing nations began pressing Tuesday to strip Europe of its traditional hold on the top job at the International Monetary Fund, as pressure mounted on embattled managing director Dominique Strauss-Kahn to resign.

Treasury Secretary Timothy F. Geithner added what may be a decisive voice to the debate Tuesday when he said during a speech in New York that Strauss-Kahn’s arrest on sexual assault charges means he is “obviously not in the position to run the IMF.” Geithner called for acting managing director John Lipsky, the agency’s No. 2, to be more formally recognized as the IMF’s interim head.

It was the most explicit statement yet by a U.S. official about the matter, and while not a direct call for Strauss-Kahn’s resignation, it added to the sense that his grip on the job is slipping.

In China, Brazil and Turkey, officials of the three large, fast-growing and influential emerging economies used Strauss-Kahn’s arrest to argue that his successor be chosen by merit and not geography, setting the tone for a potentially divisive battle over the IMF’s executive suite. European officials, struggling through a continental debt crisis and relying on the IMF for help, insist they retain the managing director’s job at least for the next few years.

But both the Brazilian and Chinese foreign ministries issued statements Tuesday saying it was time to end the World War II-era “gentleman’s agreement” that guaranteed Europe the managing director’s post. Turkey’s finance minister, meanwhile, said he felt fully qualified to succeed Strauss-Kahn, a Frenchman, and said many other economists and finance officials from developing nations could say the same.

“Our hope is that in the coming period, IMF heads will come from developing countries like Turkey, like Russia,” Turkish Finance Minister Mehmet Simsek said in an interview on the Kanal 24 television station, according to wire service reports. “As far as myself, I don’t have even the tiniest shortage in terms of experience of knowledge.”

Strauss-Kahn has been charged with seven counts and faces a possible 25-year sentence after an alleged sexual assault on a hotel worker at the Sofitel in New York City. He remains in jail at New York’s Rikers Island as a grand jury considers whether there is sufficient evidence to indict him. His next court appearance is scheduled for Friday.

While he retains his post at the IMF, there is a widespread expectation that he will resign. “We have not had contact with the managing director since his arrest in New York,” said IMF spokesman William Murray. “Obviously, it will be important to be in contact with him in due course.”

Tuesday saw the first high-level calls for him to step down. The finance ministers of Austria and Spain said Tuesday that he should consider resigning given the severity of the charges and the likelihood of a long legal battle.

At a gathering of European finance ministers in Brussels, Austrian finance chief Maria Fekter said Strauss-Kahn “has to figure out for himself that he is hurting the institution.”

Also Tuesday, Spain’s finance chief, Elena Salgado, called the allegations against the IMF chief “extraordinarily serious” and added that “if I had to show my solidarity and support for someone, it would be toward the woman who has been assaulted.”

Their comments breach what has been a general silence among officials toward the substance of the allegations against Strauss-Kahn. In France, the case has triggered outrage over what is perceived as the brusque treatment of a man who, until Saturday, was considered a top potential contender in next year’s French presidential elections.

At the same time, the arrest has resurrected prior debates about Strauss-Kahn’s relationships with women. According to European news reports, writer Tristane Banon said through her attorney that she was considering filing a complaint against Strauss-Kahn on the basis of a nearly decade-old incident in which she claims he molested her. Strauss-Kahn was reprimanded by the IMF board in 2008 for an affair with a female staffer at the agency but was allowed to keep his job.

At a Tuesday briefing, White House press secretary Jay Carney said the Obama administration had “full confidence in the IMF and its continued capacity to fulfill its obligations” under Lipsky. Carney declined to comment on whether Strauss-Kahn should remain in the IMF job or to discuss whether the United States would support a non-European successor.

The hesitancy to comment is probably appropriate at this point in the process, said Tony Fratto, a George W. Bush administration spokesman during the protracted battle over Paul D. Wolfowitz’s presidency of the World Bank, which ended in his resignation over a pay package provided to a female staffer.

Executive boards at agencies such as the World Bank and the IMF, Fratto said, tend to be passive in situations like this, preferring that top employees who get into trouble resign without being compelled to do so.

But there are risks in letting such situations linger.

“You want it resolved before the staff . . . start sending petitions saying he has to step down,” as happened with Wolfowitz, said Fratto, managing partner at Hamilton Place Strategies. “. . . There is a sense that boards do not like to fire people. . . . I am sure that is where this board is now. The problem with the situation is that he is at Rikers Island, and how do you have that discussion with him?”