French President Nicolas Sarkozy said after a meeting with German Chancellor Angela Merkel that they would prefer a treaty agreed by all 27 members of the European Union but would also accept a treaty among just the 17 countries that use the euro.
The new treaty should include automatic sanctions for countries that violate rules meant to keep government deficits in check.
Investors cheered the two leaders' comments, with the euro and stocks rising and bond yields dropping.
The meeting comes at the start of a crucial week for the eurozone, as it struggles to convince markets that it is able to solve its debt crisis.
Sarkozy said a jointly issued bond by all the countries that use the euro is not the solution to the continent's debt crisis.
Many analysts have said that only by issuing bonds backed by the whole eurozone will Europe be able to save its shared currency.
Stronger countries, like Germany and France, have resisted those calls, but some thought that as the crisis worsens they might be forced to relent. Sarkozy reiterated Monday, however, that a common bond was "in no way" the solution to the crisis.