Europe's eurozone bailout institution has approved a 2.72 billion euro ($2.88 billion) disbursement to recapitalize Greece's ailing Piraeus Bank.

The amount is part of 10 billion euros set aside for Greek banks under the country's third international bailout, which was agreed on this year.

The fund, called European Stability Mechanism, said Tuesday that Piraeus had covered about 2.2 billion euros of a 4.93 billion euro shortfall identified during recent stress tests on Greek banks, and that the stability mechanism would provide the remaining amount.

ESM head Klaus Regling said Greece had "cleared an important hurdle by securing sufficient interest for the recapitalization among private investors."

The ESM said the release of the remaining 7.28 billion euros for the banks "will be decided on a case by case basis."