The results of the ECB's tests, announced earlier on Saturday, showed that Greece's banks need to raise more than 14 billion euros (£10 billion) of extra capital to cover mounting unpaid loans.
The capital hole has emerged chiefly due to the rising number of Greeks unable or unwilling to repay their debt, after a dispute over reforms between the leftist government and international lenders almost saw Greece leave the euro.
As controls on cash withdrawals have squeezed the economy, loans at risk of non-payment have increased by 7 billion euros to 107 billion euros.
"The total capital shortfall... for the Greek banks falls well within the 25 billion euro buffer earmarked in the ESM program for bank recapitalization," a spokesman for the European Stability Mechanism (ESM), the bailout fund, said.
"It shows that the ESM program was adequately funded for this purpose and that the maximum program lending to Greece will effectively be less than the 86 billion euro initially envisaged," he said.
Within in the 86 billion, euro zone governments have earmarked a total of 25 billion euros for bank recapitalization in Greece.
But depending on the degree of participation of private investors in the recapitalization of Greek banks, the ESM's fund already raised for the purpose may be enough.
"A sum of 10 billion euros has already been mobilized and is sitting at a segregated account managed by the ESM. This will be made available quickly to Greece. With sufficient private sector participation, the remaining 15 billion euros will not be needed," the spokesman said.
(Reporting By Jan Strupczewski)
