Ministers from the 16-country euro zone announced late on Monday they had agreed the "technical modalities" that would permit aid to be rapidly rolled out but gave no figures and few details of a plan likely to involve bilateral loans.
They reconvened on Tuesday with the other finance ministers from the 27-country European Union, and the German and Spanish ministers reiterated that Greece did not need help for now.
Ministers did not say when a final decision on aid for Greece was likely. A German government spokesman said Berlin did not expect any decision to be taken at an EU summit next week.
Germany, Europe's biggest economy and the country that would be the linchpin of any support, is reluctant to bail out Greece and above all to rush into anything before Athens shows it is willing to take the painful steps needed to fix its finances.
Help for Greece could take the form of bilateral aid but ministers ruled out loan guarantees, said Jean-Claude Juncker, the Luxembourg prime minister who chaired Monday's talks.
A statement published by the euro zone ministers provided no figures. It commended Greece's redoubled efforts to repair its public finances and said the rest of the Eurogroup club of common currency countries stood ready to help.
Greece this month unveiled extra austerity measures to knock its deficit from 12.7 to 8.7 percent of gross domestic product this year, including cuts in public sector pay and tax rises. A poll on Sunday showed most Greeks saw this as a good step.
The measures and the euro zone's verbal backing have helped ease the premium Greece must offer over benchmark German bonds as it seeks to refinance some 20 billion euros ($27.5 billion) in debt coming due in April and May.
The price investors demand to hold Greek debt instead of German benchmark bonds narrowed on Tuesday morning. It came in 12 basis points in early trading, but remained close to 300 basis points, or 3 percent, above German Bund yields.