* Piraeus buys Millenium's Greek unit for 1 million euros
* BCP will invest 400 mln euros in Piraeus
* BCP gets solvency boost, no new cash disbursement
* Piraeus shares up 15 pct, BCP up 4.2 pct
* Eurobank gives up share recap plans to fall under state control (Adds Eurobank falling under state control)
By George Georgiopoulos and Andrei Khalip
ATHENS/LISBON, April 22 (Reuters) - Greece's second-largest lender Piraeus Bank has clinched a deal with a Portuguese bank to meet its fundraising targets and stay out of state hands, it said on Monday
But Eurobank, the country's fourth-biggest bank, announced that it had given up its own plans for a capital increase, preferring to fall temporarily under state control.
Greece's top four lenders need a combined 27.5 billion euros to replenish their capital after severe losses incurred during the country's debt crisis. Under the terms of Greece's international bailout they must raise at least a tenth of the capital they need from private investors or be nationalised.
Piraeus said it achieved its goal of remaining in private hands by agreeing a deal to buy the Greek assets of Millennium BCP in return for the Portuguese lender buying 400 million euros ($523 million) of Pireaus shares.
Eurobank had to pick a different course after Greece's creditors blocked its planned merger with larger rival National Bank, effectively depriving it of shareholder support.
The merger plan was well advanced, with National Bank having already taken an 85 percent share in Eurobank, when Greece, the EU and the IMF called it off on concerns that the joint entity would become too big.
Eurobank said it would work on a new business plan to return to private hands at some later point.
The deal between Piraeus and Millennium reflects efforts to consolidate the Greek banking sector into a smaller number of stronger players and is the latest in a series of Piraeus purchases.
As in previous deals, it is effectively being paid by Millennium to take the latter's Greek business off its hands.
The nominal value of the deal, which sent Piraeus shares up 15 percent, is small, with Piraeus paying only 1 million euros ($1.3 million) for the unit. The broader significance lies in BCP's participation in Piraeus's recapitalisation.
The deal will also improve the solvency ratio at Portugal's largest listed bank, by diminishing its risky assets and alleviating concerns about the need for extra capital in the bailed out country's financial sector.
Both Greece and Portugal are under international bailouts after being hit hard by the debt crisis. Greece's four largest lenders, the other one of which is Alpha Bank, need the 27.5 billion euros in fresh funds to restore their solvency ratios to levels required by the central bank after heavy losses from sovereign debt writedowns and impaired loans.
Piraeus had also planned to raise up to 400 million euros through a private share placement and up to 6.94 billion from a rights issue to boost its capital base.
Under Monday's deal BCP will take up Piraeus's private placement. Piraeus's announcement confirmed what bankers close to the deal had told Reuters on Friday.
IMPROVED CAPITAL POSITION
Piraeus said the deal would improve its capital position and profitability, helping it more than cover a 10 percent private sector participation requirement in its upcoming rights issue to remain privately run.
"We believe we can achieve an even larger private sector participation in our capital increase," the bank's Chairman Michael Sallas said in a statement.
Piraeus, which was advised on the deal by Barclays, Deutsche Bank and Lazard Freres, said BCP will recapitalise the Greek unit with 400 million euros before the sale.
BCP, whose shares rose 4.2 percent, said the deal allows it to deconsolidate about 4 billion euros in risk-weighted assets, while the recapitalisation and Piraeus's private placement do not require it to commit any new cash.
The Portuguese bank had already booked a 427 million euro provision for losses in its Greek arm, which covers the recapitalisation. The money for the Piraeus private issue will come from existing loans already granted by BCP to its subsidiary.
"With this sale, Millennium BCP gets an immediate reinforcement to its core Tier 1 (capital) of up to 100 basis points, which benefits its shares," said Andre Rodrigues, an analyst at Caixa Banco de Investimento.
This would lift BCP's core Tier 1 ratio to about 10.8 percent under European Banking Authority (EBA) criteria, well above the 9 percent minimum requirement.
The improvement comes after ratings agency Moody's warned this month that Portuguese banks may need an extra 8 billion euros in capital. The Portuguese Banking Association denied any such need and said the banks were well-capitalised.
Piraeus has already struck deals to buy the Greek branches of Cyprus's troubled banks and Societe Generale's Greek unit Geniki Bank. ($1 = 0.7644 euros) (Additional reporting by Sergio Goncalves in Lisbon and Harry Papachristou in Athens; Editing by David Holmes and David Goodman)