* Eurobank is 3rd Greek bank to tap int'l markets
* Aims to complete offering by May
* Floor price for new shares to be set on Monday
* Cannot be less than 0.30 euros
By George Georgiopoulos
ATHENS, April 12 Greece's third-largest lender Eurobank got approval on Saturday from the country's bank rescue fund, its main shareholder, for a 2.86 billion euro ($3.97 billion) share offering to plug a capital shortfall.
Eurobank expects the share offering to be completed by May, its board told shareholders on Saturday.
Eurobank will be the third Greek lender after Alpha Bank and Piraeus to tap capital markets to bolster it equity this year, as signs that Greece is starting to recover from its severe debt crisis are luring foreign investors back to battered Greek assets.
Athens returned to the bond market on Thursday after a four-year exile, raising 3.0 billion euros with a five-year bond that was snapped up by foreign investors.
Alpha Bank and Piraeus raised a combined 2.95 billion euros last month.
Eurobank, with a market value of 2.47 billion euros and 95 percent owned by the HFSF bank rescue fund, will proceed with a combined offering of new shares to international and domestic investors.
Current shareholders, including the HFSF, will waive their rights to the share issue, meaning the rescue fund's current stake will be significantly diluted.
"Eurobank will take the big step to return to private ownership," the bank's CEO Christos Megalou told a shareholders' meeting. "The capital increase will shield the bank with a capital adequacy that can meet the challenges of the future."
Eurobank's capital shortfall was revealed in a health check last month by the Greek central bank to see whether last year's 28-billion-euro recapitalisation of the top four banks had left them with enough cash to withstand rising loan losses. It showed that Eurobank needed an extra 2.95 billion euros.
Barclays, Deutsche Bank and JP Morgan will lead the bookbuilding to international investors and about 10 percent of the new shares will be offered to domestic investors, Megalou said.
The board of the Hellenic Financial Stability (HFSF) rescue fund, which pumped 5.84 billion euros at 1.54 euros a share to recapitalise Eurobank last year and became its majority owner, will convene on Monday to set a floor price for the new shares.
The price cannot be lower than 0.30 euros, the par value of the bank's existing shares, Eurobank's board said. The HFSF may set the bar a bit higher.
The rescue fund has hired Lazard and Morgan Stanley as advisers to assess a fair value for Eurobank.
Its board will evaluate bids from so-called anchor investors, who must bid for at least 1.2 billion to 1.5 billion euros worth of the offering, and make its choice on Tuesday, a senior HFSF executive told Reuters.
"A price range for the offering will be announced before books open, most likely in the next 10 days," the HFSF executive said, declining to be named. (Editing by Susan Fenton)