(Corrects date of shareholders' meeting to April 6 from April 4)
ATHENS, March 29 (Reuters) - Greece's third-largest lender Alpha Bank said on Friday it would hold a shareholders' meeting on April 6 to seek approval for a 457.1 million euro rights offering as part of a 4.6 billion euro recapitalisation to boost its solvency ratio.
Greece's four major banks need 27.5 billion euros in fresh capital to restore their capital adequacy to levels required by the country's central bank after incurring big losses from a sovereign debt writedown and impaired loans.
Most of the funds will be provided by a state bank support fund - the Hellenic Financial Stability Fund (HFSF) - in exchange for new shares or contingent convertible bonds or so-called CoCos.
Alpha said in a bourse filing it would also seek shareholder approval to raise another 92.9 million euros by issuing new common shares with existing shareholders waiving their rights. These shares would be privately placed.
Greece's international lenders have set aside 50 billion euros from the country's bailout package to recapitalise its viable banks and cover the costs of winding down others that are deemed non-viable.
Alpha's capital need was set by the Bank of Greece at 4.6 billion euros.
The remaining 4.05 billion euros the bank needs will be supplied by the HFSF in exchange for new shares. (Reporting by George Georgiopoulos; Editing by Pravin Char)