ATHENS--One of Greece's largest lenders, Eurobank Ergasias SA, has secured nearly half of the roughly EUR3 billion ($4.1 billion) it needs to plug a hole in its balance sheet, the country's bank-rescue fund said Tuesday.

The Hellenic Financial Stability Fund said in a news release that a group of investors--including Canadian investment firm Fairfax Financial Holdings Ltd., Capital Research and Management Co., Wilbur Ross & Co., Fidelity management and Research Co., Mackenzie Financial Corp. and Brookfield International Bank Inc.--committed to subscribe for 47%, or EUR1.3 billion, of Eurobank's share offering.

Later Tuesday, the board of the country's largest lender by assets, National Bank of Greece, is expected to confirm a plan to cover a roughly EUR2.3 billion shortfall in its balance sheet.

The Bank of Greece last month said the four main Greek lenders--National Bank of Greece SA, Piraeus Bank SA, Alpha Bank AE and Eurobank--needed nearly EUR5.8 billion in additional capital.

Greece's banks have been battered heavily by the country's six-year recession, a steep decline in Greek property prices and an unprecedented EUR200 billion sovereign-debt restructuring in early 2012.

Last 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.

Although the bad loans continue to rise and aren't expected to peak until late this year, efforts by Greek lenders to raise fresh funds from foreign investors appear to be paying off.

The move by Eurobank and eventually by NBG follows the example of the country's other two systemic banks-- Piraeus and Alpha--which raised EUR1.75 billion and EUR1.2 billion, respectively, in late March.

Eurobank, currently 95% owned by the country's rescue fund, faced the biggest shortfall--requiring some EUR2.9 billion.

The lender 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.

"The remaining amount of the capital Increase will be covered via a book building process for international and other qualified investors and a public offering in Greece," HFSF said in the new release.

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

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