With global leaders preparing for next month's Group of 20 nations (G20) summit in Cannes, France, the International Monetary Fund — of which the U.S. is the greatest contributor — is being relied on to help underwrite whatever efforts are needed to backstop toxic European sovereign debt.

Geithner said the International Monetary Fund (IMF)has "very substantial" resources to fund a device that could look like the Troubled Asset Relief Program, which helped navigate American financial institutions through the crisis in 2008 and 2009.

"Through the IMF, of course, we're already playing a very major role," he said in a live interview in Paris. "We're happy to see the IMF continue to play that role in support of a more forceful, comprehensive strategy where Europe's own resources—very ample resources—are deployed on a much more substantial scale."

The comments give a lift to U.S. stocks, which have been highly volatile in the past several months as proposed solutions have come and gone for the euro crisis.

Geithner declined to give a specific number on what would be required to aid Greece and any other potential countries that need help meeting their obligations.

Estimates have run as high as $2 trillion for a liquidity fund, and Geithner said that whatever the figure is, it should leave no doubt that there will be more than enough.

"A basic rule of financial crises management is you want to make sure you have a level of resources that are larger than the potential need you face," he said. "If markets see that then they'll have the incentive to continue to lend, invest, to get more exposure to those countries."