PARIS—Despite increasingly loud offers of assistance from emerging economies in the International Monetary Fund, a fix for Europe's debt crisis appears likely to remain firmly in the hands of the Europeans.

A handful of emerging-market officials, showing off their growing swagger on the international stage, headed into a meeting of finance ministers and central bankers from the Group of 20 industrial and developing economies suggesting they could assist the IMF with new resources to help bail out Europe.

Several officials from Brazil, Russia, India, China and South Africa had spurred similar speculation last month ahead of a G-20 meeting in Washington, and will likely keep up their message at the next gathering in November.

But at the meeting held this weekend, the IMF's leading powers swatted down the idea repeatedly. Finance ministers from the U.S., Germany, Japan, Canada and others say Europe can fund its own bailout.

"Our view is that the tools are sufficient within Europe to deal with what is after all a European problem, in the euro zone, of relatively wealthy countries," Canadian Finance Minister Jim Flaherty said.

The debate shows how rising economic powers, particularly China and Brazil, are trying to gain more influence on a global stage. With their economies in relatively better shape than those in much of the developed world, there remains the tantalizing prospect these countries might serve as saviors for a debt crisis that threatens to derail the world economy.

Chinese Vice Finance Minister Zhu Guangyao said talks about boosting the IMF's resources are continuing and "all options are on the table." Brazilian Finance Minister Guido Mantega said he held discussions with other G-20 nations "to see what we can do."

Created in the aftermath of World War II, the IMF has traditionally served as the world's crisis lender. It has about $390 billion available today, hardly enough to rescue Europe. The IMF's own staff has stoked speculation that more could be on the table by working on proposals for new programs that could be funded in part by big emerging countries.

But the U.S., the largest IMF shareholder, is so firmly against boosting IMF resources to deal with the current crisis that Treasury Secretary Tim Geithner didn't even stop to debate the issue with other officials inside the G-20 meetings. Some G-20 officials fear a leading IMF role, even if it could be agreed upon, would relieve pressure on Europe to act on its own.

Advanced economies left the door open for the IMF to eventually take a smaller, supporting role.

"The IMF has substantial additional uncommitted financial resources and if the circumstances are right, we support deploying those," Mr. Geithner said after the meetings.

Europe initially resisted the IMF's involvement when the crisis flared in early 2010 because they didn't want to cede control. The IMF ultimately provided some funding to support the bailouts of Greece, Portugal and Ireland. Top European officials have been generally pleased with the IMF's involvement, because the organization has served as an enforcer of the bailout's terms.

The G-20 debate about deploying IMF resources for Europe is akin to a "poker game," said John Kirton, co-head of the University of Toronto's G-20 Research Group. Advanced countries such as the U.S. and Canada first want to see euro-zone leaders deliver an aggressive strategy. "If there's a credible plan, then, and only then, will there be money," Mr. Kirton said. "They don't want to let Europe off the hook."

IMF Managing Director Christine Lagarde told reporters that the IMF would propose one new program at the full G-20 Cannes summit in November: a short-term lending facility to help shelter strong economies from economic shocks.