World leaders continue to wrangle over proposals to give the International Monetary Fund hundreds of billions of dollars to battle the European financial crisis, with a top U.S. official insisting Thursday that the money isn’t needed.

Lael Brainard, undersecretary of the Treasury for international affairs, said in testimony to the Senate banking committee that the IMF’s financial stake in Europe should remain limited, even as the agency continues providing technical advice and overseeing programs in Greece and other struggling countries in the region.

“The challenge Europe faces is within the capacity of the Europeans to manage, and the administration has been clear with our international partners that we are not seeking additional funding for the IMF,” Brainard said in prepared remarks. “IMF resources cannot substitute for a strong and credible European . . . response.”

Her remarks are part of a global tug of war over how to pay for Europe’s problems and insulate the world from the economic fallout if conditions worsen.

World economic officials agree more money should be set aside for the purpose. The IMF is seeking about $500 billion as a precaution in case the euro zone’s debt problems intensify.

But as officials head toward high-level economic meetings next week in Mexico, they have yet to resolve the issue of where the money should come from.

Domestic politics weighs on leaders in the United States and elsewhere. Even if the Obama administration wanted to provide more money for Europe or the IMF, it would be tough in an election year when U.S. government deficits are an issue and Republican presidential candidates are dismissive of helping Europe.

There are also worries about equity — why should the developing economy of India subsidize the advanced economy of Italy? — and technical concerns about the IMF becoming a conduit for spreading credit risk around the world.

U.S. officials argue that if the 17 nations of the euro area — collectively wealthy and anchored by major powers like Germany and France — pledged hundreds of billions of dollars to stemming the spread of the Greek financial contagion to other countries, investors would be reassured, and the crisis would be over.

Emerging giants like China have expressed a willingness to contribute more to the IMF, and they have a vested interest in seeing the European crisis fixed before it further drags down trading with the region. But they have largely taken their cue from the United States, the IMF’s largest shareholder, remaining on the sidelines and encouraging Germany and others in Europe to do more for themselves.

European officials are increasingly vocal that their own taxpayers feel tapped and that the world — and the United States — should up the ante.

“What we are seeing in Europe is not just a European crisis,” Luxembourg’s finance minister, Luc Frieden, said in Washington this week, repeating an argument often heard in Europe that if not for the deep round of financial problems that began in the United States in 2008, Europe would not be in its current state. European governments were forced to borrow in response to that previous crisis, contributing to the current public debt burden, the argument goes. And the region’s financial companies were stuck with large amounts of bad loans, contributing to the current troubles in Europe’s banking system.

The disagreement over how to build a “firewall” to stop the spread of Greek contagion is in addition to the ongoing debate over Greece itself.

Two years into that country’s crisis, euro-zone leaders are still struggling with how best to help the country and pay the tab. Talks over a new Greek plan continue as officials debate how much more public money should be lent to Greece, how much private investors should contribute through losses on their Greek bonds, and how much Greece itself must absorb by cutting government spending and raising taxes.

So far, euro-zone countries have been hesitant to increase their contribution to Greece — Germany’s finance minister has referred to the country as a “bottomless pit” — or even to pay money already promised. Euro-zone governments pledged $200 billion to the IMF in December, but that money remains unpaid while the rest of the world debates whether it will participate at all.

The struggle points to a larger debate developing around the fund.

Outside critics note the rising amounts of money the agency has loaned already to bailouts of Greece, Ireland and Portugal — and question the potential conflicts involved in an international agency traditionally dominated by Western European managers and economists subsidizing that region. Others see the loans to Europe as a dangerous expansion of the fund’s mandate — from stabilizing economies that need comparatively short-term help to global lender of last resort for countries in need of long-term economic restructuring.

In recent columns published in the Financial Times, former European Central Bank board member Lorenzo Bini Smaghi has argued that the Greek crisis shows the need for an overhaul of the IMF. The agency, he said, must be able to delve deep into the problems of developed nations and, if necessary, support long and costly efforts to restructure their economies.

“Crises in advanced economies may develop in very different ways from those of past crises in developing or emerging economies,” Smaghi wrote. “The options available to the IMF may need to be rethought.”