“Other countries are no longer willing to buy into the idea that the U.S. knows best on economic policy, while at the same time the emerging markets have become increasingly influential and independent,” said Kenneth S. Rogoff of Harvard, a former chief economist at the I.M.F.

The inconclusive I.M.F. outcome means that the renminbi’s exchange rate will again be a focus when President Obama and other leaders of the Group of 20 economic powers gather next month in Seoul, South Korea. Officials said the United States would keep up pressure on China in the weeks leading up to that meeting.

Despite the bland language of the I.M.F. statement on Saturday, American and European officials said the weekend meetings were not a failure.

After all, the 187-member I.M.F. is not a customary forum for decisive collective action, and changes in national economic policies typically occur in a gradual, incremental fashion. A Treasury official pointed out that the gatherings focused high-level attention on the currency problem, and ended with an agreement for the I.M.F. to play a greater role in monitoring its members’ exchange-rate practices and the “spillover effects” of each country’s economic policies on the rest of the world.

Even so, economic and political forces have made it difficult for the United States to address what Mr. Geithner has called the “central existential challenge of cooperation.”

“Even though this is inherently a collective problem, there is no specific mechanism in the I.M.F. or G-20 that looks up to the challenge,” he said Sunday. “Our aim is to change that by encouraging countries to buy into a stronger set of norms and behaviors on these issues.”

In a speech on Wednesday, Mr. Geithner in essence accused China of setting off a cycle of “competitive nonappreciation,” in which countries block their currencies from rising in value to support their exporters  as Japan, Brazil and South Korea have recently tried. Economists have warned that this type of policy could lead to a destructive currency war.