The IMF and many economists, however, fret that an extension and fresh loans alone still won't be enough and that Greece's eurozone creditors might have to forgive some of their debt.
"We cannot help the country with loans alone," Asmussen insisted. "That closes the financing gap but at the same time increases the country's debt."
Germany's influential central bank chief Jens Weidmann, who also sits on the ECB's governing council, said Friday that Greece will need another debt write-off, a so-called haircut, at the end of a long reform path to make its debt sustainable again.
Earlier this year, Greece reached a deal with private creditors to wipe some â¿¬100 billion off the national debt.
But forgiving some of its public debt is an option that is unpalatable to many political leaders across Europe because they oppose the idea of telling voters that billions in taxpayers' money will be lost.
"That is impossible," insisted German Finance Minister Wolfgang Schaeuble in an interview with German broadcaster ARD.
Instead, he again urged Greece to do its homework and push through the budget cuts and structural reforms, saying it has "decided but not yet implemented them."
Schaeuble added that telling Greece now that its creditors will eventually foot the bill would reduce the country's incentive to reform and could therefore be self-defeating because the crisis' underlying causes wouldn't be addressed.
"Greece cannot be spared the path of regaining competitiveness through structural reforms," he added.
When pressed to say how much rescuing Greece will eventually cost German taxpayers, Schaeuble said: "Nobody knows that exactly."
Juergen Baetz can be reached on Twitter at http://www.twitter.com/jbaetz