ATHENS--Greece's four big, systemic banks will need another 6.4 billion euros ($8.9 billion) to shore up their still-fragile balance sheets, the country's central bank said Thursday, in order to cope with an ever-growing mountain of bad loans that have become yet another painful legacy in Greece's protracted debt crisis.

In a statement, the Bank of Greece said the four banks-- National Bank of Greece SA, Piraeus Bank SA, Alpha Bank AE and Eurobank Ergasias SA--would need to present plans by mid-April how they would raise that capital; such as by selling down assets, going to the capital markets or else by appealing for further state aid.

Eurobank, already under state control, faces the biggest shortfall--it needs another EUR2.9 billion in capital--followed by market leader National Bank of Greece, which must raise some EUR2.2 billion, the central bank said. Piraeus and Alpha Bank followed, with the former facing a EUR425 million shortfall, and the latter needing EUR262 million.

After a deep, six-year recession, a pricked property bubble, flight among depositors, and an unprecedented EUR200 billion sovereign-debt restructuring, Greece's banks are in a world of hurt. This year, they were recapitalized with the help of a European Union loan, but together they still hold some EUR70 billion in bad loans--a sum equal to a third of Greece's gross domestic product.

Write to Alkman Granitsas at alkman.granitsas@wsj.com and Nektaria Stamouli at nektaria.stamouli@wsj.com

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