ATHENS-- Piraeus Bank SA said Wednesday it had completed a EUR1.75 billion share capital increase, the second by a Greek bank this week, signaling a growing confidence by foreign investors in the nation's banking sector.

The announcement by Piraeus, Greece's largest domestic lender by assets, comes just a day after smaller rival Alpha Bank AE announced the completion of a separate EUR1.2 billion capital increase following a successful placing of its shares with foreign investors.

"We would like to thank the international investment community for its great response and its trust towards the prospects of Piraeus Bank, the Greek banking sector and the Greek economy," Piraeus Bank Chairman Michalis Sallas said in a news release. "We would like to congratulate Alpha Bank for its big success in the share capital increase process. We believe that both capital raises are of historical importance for the Greek banking market and will contribute significantly to the recovery effort of the Greek economy."

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, Greek lenders 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 those bad loans continue to rise and aren't expected to peak until late this year, efforts by Greek lenders to raise fresh funds appear to be paying off. Last week, Piraeus Bank raised half a billion euros via a bond issue, the first bond issued by a Greek bank since the country's debt crisis erupted at the end of 2009.

In a bid to shore up their fragile balance sheets and cope with the mountain of bad loans, Greece's central bank told Piraeus and Alpha Bank earlier this month that they need to raise EUR425 million and EUR262 million, respectively. The country's four big lenders--which includes Piraeus and Alpha, as well as National Bank of Greece SA and Eurobank Ergasias SA--need to cover a total capital shortfall of EUR5.8 billion.

Eurobank, now under state control, faces the biggest shortfall--requiring EUR2.9 billion. It has announced plans to move ahead with a EUR3 billion share capital increase to cover its needs. NBG, which needs to plug a EUR2.2 billion hole in its balance sheet, says it can raise the money without selling more shares.

In its statement, Piraeus said it had placed roughly a billion new ordinary shares at EUR1.70 each, a discount of 10% to its closing price Wednesday. A shareholders' meeting will be held Friday to formally approve the equity offering.

On Tuesday, Alpha Bank said it had placed its shares at EUR0.65 each, a discount of 7% to Monday's closing price. Alpha has also called a shareholders' meeting Friday to formally sign off on the capital increase.

"The degree of participation, and the relatively small discounts, suggest a strong vote of confidence for the prospects of the Greek economy and the banking sector," said Panagiotis Kladis, analyst at NBG Securities.

Write to Stelios Bouras at stelios.bouras@wsj.com

Subscribe to WSJ: http://online.wsj.com?mod=djnwires