Given the inevitability that these countries will have a growing influence, the London summit meeting, which begins Thursday, is likely to be remembered “as the last hurrah for the U.S. and Europe rescuing the world economy,” said Simon Johnson, a professor at M.I.T. and a former chief economist of the fund.

One reason the I.M.F. has emerged as such a popular cause is that the United States has been unable to rally countries behind its other major priority: economic stimulus. The European Union opposes further stimulus packages in 2010, arguing that its social safety net makes an increase in government spending unnecessary.

European and American officials are also still divided, to a lesser degree, on how to rewrite international financial regulations. France and Germany are more receptive than the United States to giving regulators supranational authority to scrutinize global banks and other financial companies.

“The United States is desperately trying to assert leadership, as if it were 10 years ago, when the U.S. set the agenda,” said Kenneth S. Rogoff, an economist at Harvard and another former chief economist of the fund.

With more countries slipping into crisis by the week, there is general agreement that the fund needs additional resources. Since last year, the I.M.F. has made nearly $50 billion in loans to 13 countries. It is streamlining the process for making loans and loosening its strings, hoping to counter the resentment that built up against it during past crises because of its stringent demands.

At a preparatory meeting two weeks ago, finance ministers of the Group of 20 agreed to “very substantially” increase financing, though the Europeans favored an extra $250 billion, not $500 billion.

Whatever their reservations about financing, the Chinese have seized on the fund for another purpose: to tweak the United States. The governor of China’s central bank, Zhou Xiaochuan, recently proposed that the American dollar be phased out as the world’s default reserve currency. As a replacement, he suggested using special drawing rights, or S.D.R.’s, the synthetic currency created by the fund that is used for transactions between it and its 185 member countries.