PARIS — European leaders rushed Monday to stop a rampaging debt crisis that threatened to shatter their 12-year-old experiment in a common euro currency and devastate the world economy as a result.

One proposal gaining prominence would have countries cede some control over their budgets to a central European authority. In a measure of how rapidly the peril has grown, that idea would have been unthinkable even three months ago.

More relevant to the crisis, borrowing costs for European nations stabilized. They had risen alarmingly in recent weeks — in Greece, then in Italy and Spain, then across the continent.

Allowing a central European authority to have some control over the budgets of sovereign nations would create a fiscal union in Europe in addition to the monetary union of the 17 countries that share the euro currency.

Some analysts have said would be a leap toward creating a United States of Europe. More delicately, it would force the nations of Europe to swallow their national pride, cede some sovereignty and agree to strengthen ties with their neighbors rather than fleeing the euro union during the crisis.

“The common currency has the problem that the monetary policy is joint, but the fiscal policy is not,” Germany’s finance minister, Wolfgang Schaeuble, said in a meeting with foreign reporters in Berlin.

The monetary union has existed since the euro was created in 1999, but the European Union, which includes the 17 euro nations and 10 others that use their own currencies, has no central authority over taxing and spending.

A fiscal union could prevent excessive spending in the future. More important, it would be a step toward addressing today’s debt crisis: It could provide cover for the European Central Bank to stage a massive intervention in the European bond market to drive down borrowing costs and keep the debt crisis under control.

Enforced budget discipline might ease the ECB’s concerns about the concept known as moral hazard — essentially, that bailing out free-spending countries would only encourage them to do it again.

A fiscal union would also pose a practical problem — how to make such a body democratically accountable.

Another option is for the 17 nations in the euro group to sell bonds together, known as eurobonds, to help the countries in the deepest trouble because of debt. Germany has resisted such a plan, because it would raise borrowing costs for it and other nations that good credit ratings.

While Europe buzzed over the possible solutions, European finance ministers prepared for a summit beginning Tuesday evening in Brussels, and Italy readied an auction of bonds designed to raise euro8 billion, or about $10.6 billion — and steeled itself for the high interest rates it will have to pay.

Already, the Organization for Economic Cooperation and Development, an international group devoted to economic progress, was warning that the global economy was in for a rocky road in coming months.