Davos, Switzerland ? The head of the International Monetary Fund appeared to be making headway Saturday in her drive to boost the institution’s financial firepower so that it can help Europe prevent its crippling debt crisis from further damaging the global economy.

Christine Lagarde, who replaced Dominique Strauss-Kahn as managing director of the fund six months ago, is trying to ramp up the IMF’s resources by $500 billion so it can help if more lending is needed in Europe or elsewhere. The IMF is the world’s traditional lender-of-last-resort and has been involved in the bailouts of Greece, Ireland and Portugal.

Insisting that the IMF is a “safe bet” and that no country had ever lost money by lending to the IMF, Lagarde argued that increasing the size of the IMF’s resources would help improve confidence in the global financial system. If enough money is in the fund the markets will be reassured and it won’t be used, she said, using arguments similar to those that France has made about increasing Europe’s own rescue fund.

Her plea appeared to find a measure of support from ministers of Britain and Japan, sizable IMF shareholders that would be expected to contribute to any money-raising exercise.

George Osborne, Britain’s finance minister, said there is “a case for increasing IMF resources and … demonstrating that the world wants to help together to solve the world’s problems,” provided the 17 countries that use the euro show the “color of their money.”

European countries have said they’re prepared to give the IMF $150 billion, meaning that the rest of the world will have to contribute $350 billion. However, many countries, such as Britain and the U.S., want Europe to do more, notably by boosting its own rescue fund.

Japan’s economy minister, Motohisa Furukawa, said his country would help the eurozone via the IMF, too, even though Japan’s own debt burden is massive. Unlike Europe’s debt-ridden economies, Japan doesn’t face sky-high borrowing rates, partly because there’s a very liquid domestic market that continues to support the country’s bonds.

Europe once again dominated discussions on the final full day of the forum in Davos. Despite some optimism about Europe’s latest attempts to stem the crisis, fears remain that turmoil could return.