Greece's top lender National Bank on Wednesday said it would ask its shareholders to approve a capital increase of up to 2.5 billion euros ($3.5 billion) next month.
"The board has decided to call an extraordinary general meeting on May 10 to approve a share capital increase... of up to 2.5 billion euros," the bank said in a statement.
All four of Greece's main lenders have been told by the central bank to shore up their balance sheets against mounting bad loans.
The Bank of Greece last month said Greece's four top banks -- National Bank, Piraeus, Alpha and Eurobank -- between them needed nearly 6.4 billion euros in additional capital.
National Bank's needs were estimated at 2.183 billion euros.
Its shares closed down 2.3-percent on Wednesday at 2.97 euros.
The banks' restructuring is likely to affect upcoming talks in the autumn on how to make Greece's still-massive public debt sustainable.
Eurobank's board on Saturday approved a 2.86-billion-euro capital increase. On Tuesday, the Hellenic financial stability fund approved an offer by a group of investors for nearly half that sum -- 1.332 billion euros.
Investors include Fairfax, Capital Research and Management, Wilbur Ross, Fidelity, Mackenzie and Brookfield, said the stability fund, which is charged with protecting the Greek banking system.
Two other top banks -- Piraeus and Alpha -- have respectively raised 1.75 billion and 1.2 billion euros.
Greece's banking system was recapitalised last year as part of the Greek EU-IMF bailout.
A 50-billion-euro slice of the bailout was earmarked to shore up the balance sheets of the troubled lenders, which suffered heavy losses when privately-held Greek government bonds were written down in 2012.
Eurobank was unable to attract enough private funds last year and was recapitalised by the state.
There are now some 11 billion euros left in Greece's EU bank rescue package, and Athens would like to use the money to meet upcoming needs and avoid a new bailout loan.
The International Monetary Fund has said that Greece will need help in meeting a finance shortfall in 2016.
The country was rescued by the EU and the IMF with two loans totalling 240 billion euros to meet its annual running costs and finance its bond repayments.
Despite the 2012 rollover assisted by the banks, however, Greece's public debt stands at over 318 billion euros, up from 280 billion in 2012.
A new bond haircut has been ruled out, but Greece is hoping to secure a further repayment extension in the autumn as most of the debt is in the hands of official, rather than private, creditors.