The Bank of Greece, the country's central bank, plans to ask banks to boost their capital adequacy ratio to ease market fears over the impact of a haircut on Greek government bonds they hold, a Greek newspaper said on Sunday.

Battered by the country's debt crisis, Greek lenders have lost access to interbank funding and became dependent on the European Central Bank (ECB) for liquidity. Central bank authorities want to gradually wean them off this facility.

The head of the Bank of Greece, after the results of stress tests at the end of June will ask banks to strengthen their Core Tier 1 ratios, Kathimerini newspaper said, citing banking sources.

The minimum ratio of Core Tier 1 equity and reserves capital to risk-weighted assets the central bank will require will depend on the haircut assumption it will make as regards bank's holdings of Greek government bonds.

This does not mean that the Bank of Greece accepts there will be a haircut. On the contrary, as a member of the European Central Bank it is against any type of debt restructuring, Kathimerini said.

It said the central bank believes a stronger equity base may make banks' return to wholesale funding markets easier and limit their recourse to eurosystem facilities as Athens implements a fiscal plan agreed with its international lenders.

So far, National Bank and Piraeus Bank have already boosted their capital with cash calls and EFG Eurobank has sold most of its stake in Polish subsidiary Polbank to Raiffeisen..

Alpha Bank also plans a convertible bond and a rights offering of up to 2.5 billion euros and will seek shareholder approval at its June 21 annual meeting.

Banks that find it hard to beef up their capital to meet the new requirement may have to turn to the Financial Stability Fund (FSF) -- a 10 billion euro safety net set up to support the country's lenders, the paper said.

With rising bad loans, continued sovereign debt downgrades and a protracted recession taking a toll on Greek banks, authorities set up the FSF to be ready to provide capital.

Funded in stages up to 10 billion euros, the FSF is part of a 110 billion euro emergency loan package that debt-laden Greece secured from the IMF and its euro zone partners last year to avoid default.

Banks can get capital injections by issuing preferred shares to the FSF.

ECB funding to Greek banks reached 87.9 billion euros ($128 billion) in March, easing 2.8 percent from the previous month. ECB funding almost doubled to 97.6 billion euros in 2010.

(Reporting by George Georgiopoulos; Editing by Greg Mahlich)