* Proposes share swap of 58 NBG shares per 100 Eurobank shares
* Merger would form Greece's biggest lender * Eurobank says will consider proposal
(Updates with NBG public offer, Eurobank response, statement by NBG's CEO)
By George Georgiopoulos and Lefteris Papadimas
ATHENS, Oct 5 (Reuters) - National Bank of Greece made a share-swap offer to buy all of rival Eurobank and create the country's biggest lender, it said on Friday, the latest move in efforts to consolidate the Greek banking industry.
Greek banks are under pressure to merge after suffering steep losses from the country's debt restructuring, heavy deposit withdrawals and rising bad loans, but short of cash they have no option but to swap shares in order to merge.
"We are convinced that Eurobank's board will see the value our public offer creates and will propose the transaction to Eurobank's shareholders," National Bank's chief executive, Alexandros Tourkolias, said in a statement.
NBG is offering 58 new shares for every 100 shares of Eurobank. Once the share exchange is completed, NBG shareholders will own 75 percent of the combined entity, with Eurobank shareholders owning the rest.
At current prices, NBG's market capitalisation is 3.2 times that of Eurobank.
Eurobank, advised by Barclays, Deutsche Bank and Goldman Sachs International, said in a news release that it would consider the proposed merger "in a constructive spirit."
Eurobank shareholders representing 43.6 percent of the bank's stock had accepted the offer, said NBG, which is advised by Credit Suisse.
NBG Chairman George Zanias and Tourkolias would keep the same posts in the combined group, NBG said.
The bourse suspended trading in the shares of National Bank and Eurobank earlier on Friday following a media report of the merger talks, which sent Eurobank's shares up 5.5 percent to 1.15 euros and National Bank's 4.5 percent to 2.1 euros, to value the two at around 2.6 billion euros ($3.4 billion).
"Such a deal would change the Greek banking landscape, forming a European-size player with better prospects to regain access to capital markets and money markets in particular once the crisis stabilises," said Theodore Krintas, head of wealth management at Attica Bank.
Recapitalised with 18 billion euros derived from the country's international rescue fund, the country's four biggest banks - National, Eurobank, Alpha and Piraeus
- have already begun the process of consolidation by buying up smaller rivals.
Without access to interbank funding, Greek banks have relied on the European Central Bank and the Bank of Greece to relieve their liquidity squeeze. Their exposure to the Eurosystem of euro zone central banks stood at 131.6 billion euros in August.
"The banking system is adjusting faster than people expected to the overall restructuring the Greek economy has to go through. A deal will have a positive market impact, showing that things are moving," Krintas said.
A merger between National and Eurobank would create the biggest single bank in terms of loans, deposits and branch networks, with 109 billion euros in net loans, 89 billion in deposits, 178 billion in assets and a domestic network of 944 branches, said analyst Maria Kanellopoulou at Euroxx Securities.
National Bank has already tried to merge with Alpha twice, but Alpha has now reached a deal to buy French lender Credit Agricole's ailing Greek unit, Emporiki Bank, beating NBG and Eurobank which were also interested.
Piraeus took over the healthy part of troubled state lender ATEbank in July and is expected to close a deal with Societe Generale soon to buy the French bank's loss-making Greek affiliate, Geniki .
A merger would need approval from the Bank of Greece and the Hellenic Financial Stability Fund (HFSF), the bank support fund that has started to recapitalise the country's viable banks.
The HFSF bank support fund is due to be allocated 25 billion euros from the next 31.5 billion euro tranche of Greece's international bailout to carry out the banking sector's further recapitalisation.
National and Eurobank own 6 percent stakes in small state-controlled lender Hellenic Postbank (TT) , which the government decided in August was not viable. TT could end up being absorbed by the combined group according to the news site.
Including TT in the deal could help lower the capital needs of the combined entity, meaning the HFSF would have to dish out smaller amounts, Krintas said.
"The new bank that would be formed will have a very strong presence in Greece and synergies in southeastern Europe which will mean savings," said Natasha Roumantzi, a banking analyst at Piraeus Securities.
NBG has a big presence in Turkey through its subsidiary, Finansbank, and both banks also have interests in Bulgaria, Romania, Serbia and Cyprus. ($1=0.7689 euros)
(Editing by Greg Mahlich, David Holmes and Matthew Lewis)
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Keywords: NBG EUROBANK/