MEXICO CITY — As finance ministers from the Group of 20 countries began a two-day meeting here dominated by the European sovereign debt crisis, the United States was adamant that European nations must do more to buffer their economies.

At the center of the dispute is the reluctance of cash-rich economies like China and Japan to contribute new money to the International Monetary Fund without a commitment from European countries to expand their own stabilization fund first. The United States has said that it will not contribute new money to the I.M.F.

The issue of that “European firewall” is dominating the discussions here among finance ministers and the heads of central banks of the leading economies.

Treasury Secretary Timothy F. Geithner said Saturday that although European countries had made progress over the past few months in averting a “catastrophic financial failure,” more work was needed to “put in place a stronger, more credible firewall.”