ATHENS--Greece's third largest lender, Eurobank Ergasias SA, Friday announced plans to move forward with a EUR3 billion ($4.13 billion) share capital increase to cover its basic capital needs.

The bank said its board of directors has already been convened to decide on the calling of an extraordinary general meeting.

This comes a day after the country's central bank said Greece's four biggest banks will need another EUR5.8 billion to shore up their fragile balance sheets and cope with a mountain of bad loans that have become another painful legacy of Greece's protracted debt crisis.

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

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

Eurobank fell under state control last April, as it dropped plans to raise money from investors and the Hellenic Financial Stability Fund fully covered a EUR5.8 billion share issue.

After a deep, six-year recession, the collapse of a property bubble, withdrawals by depositors and a EUR200 billion sovereign-debt restructuring, Greece's banks are struggling. 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 annual gross domestic product.

With bad loans still rising and not expected to peak until late this year, the Bank of Greece had commissioned outside consultant BlackRock Solutions to assess the banks' loan portfolios, something the firm also did in 2011.

Write to Nektaria Stamouli at nektaria.stamouli@wsj.com

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