* Says Eurobank will not tap rescue fund to plug hole
* Urges National Bank to raise capital from markets (Adds National Bank, background)
By Harry Papachristou
ATHENS, April 11 (Reuters) - Greece's central bank chief George Provopoulos said on Friday he would accept a second term at the helm of the Bank of Greece if the government offered it to him when his current one expires in June.
Asked in an interview on private television station Skai if he wanted to keep his post for another six years, Provopoulos said: "Yes, I am on active service," adding this was a decision for the government of Prime Minister Antonis Samaras to make.
Provopoulos is also member of the European Central Bank's Governing Council. The 63-year-old is overseeing the recapitalisation of Greece's banking system under the terms of the country's international bailout.
In the interview, Provopoulos said he expected Greece's third-biggest lender Eurobank to raise from private investors all the funds it needs to plug a capital gap.
"I am optimistic that it (Eurobank) will raise all the money it needs from capital markets," Provopoulos said.
Eurobank is planning a capital increase of up to 3 billion euros ($4.2 billion). If it fails, it will have to tap Greece's bank bailout fund HFSF, which is funded by the European Union and the International Monetary Fund and currently owns 95 percent of Eurobank.
The HFSF has been endowed with 50 billion euros from Greece's bailout. It has 11 billion euros remaining after a first wave of bank recapitalisations last year. The less it spends to replenish Greek banks' capital, the lighter Greece's debt load becomes.
Greek banks must raise an extra 6.4 billion euros to shield themselves from a wave of bad loans created by the country's debt crisis and six-year recession.
To replenish their capital, banks can divest assets, tweak business plans to extract more cost savings or proceed with cash calls. The HFSF, which is already the majority owner of the top four lenders, is serving as a backstop in case they cannot raise enough capital themselves.
Piraeus Bank and Alpha Bank, Greece's second and fourth-largest lenders respectively, have already plugged their capital needs from the market without resorting to the HFSF.
Eurobank has the biggest capital needs of Greece's top four, systemic lenders. National Bank, the biggest, has said it will plug its gap without a cash call on investors, most probably by selling assets and cutting costs.
Speaking in the interview, Provopoulos urged National to follow the example of its three peers and try to raise capital from markets. "If it (National) also decided to tap markets, it would meet with great success," he said. ($1 = 0.7201 Euros) (Additional reporting by Lefteris Papadimas; editing by Andrew Roche)