* NBG 9mo net loss widens 82 percent to 2.45 billion euros
* Provisions shoot up 43 percent to 1.87 billion
* Alpha loss widens to 711.8 mln after 1.2 bln provs
* Alpha sees capital need at 4.6 bln, NBG's at 9.7 bln (Adds Alpha economist comment, details, background)
By George Georgiopoulos and Lefteris Papadimas
ATHENS, Dec 21 (Reuters) - Greek banks National and Alpha posted wider nine-month losses as the debt-laden country's deep recession pounded their loan books and higher funding costs squeezed net interest income.
With the economy shrinking at an annualised rate of nearly 7 percent in the third quarter, and with one in four Greeks jobless, borrowers are having a hard time servicing their debts, forcing banks to take hefty provisions for potential loan losses.
National Bank, the country's largest lender, said its net loss widened 82 percent to 2.45 billion euros ($3.2 billion) in the nine months through September.
Its provisions shot up 43 percent to 1.87 billion euros.
Alpha, Greece's No.3 bank by assets, said its loss had widened by 25.6 percent from a year ago to 711.8 million euros.
It said net interest income fell 16.4 percent, hurt by the higher cost of funding under the Greek central bank's so-called emergency liquidity assistance (ELA).
The bank, which in October agreed to buy Emporiki Bank from French lender Credit Agricole, said provisions for impaired credit rose 41.5 percent to 1.17 billion euros.
Tough conditions are seen persisting in 2013, with the economy projected to contract for a sixth straight year, meaning a further rise in non-performing loans.
"Unemployment will continue to climb in 2013, so probably non-performing loans will peak sometime in 2014," Alpha's chief economist Michael Massourakis told Reuters.
Last month Greece passed a 13.5 billion euro austerity package of budget cuts and tax hikes for the next two years, aiming to unlock bailout aid and hit a primary budget surplus in 2013.
Greece and its international lenders have earmarked 50 billion euros from the country's 130 billion euro bailout to recapitalise viable banks, whose equity capital was wiped out after participating in a sovereign debt swap in March.
Under the plan, banks will have to issue new shares to achieve a core Tier 1 capital solvency ratio of at least 6 percent and convertible bonds or CoCos to boost the ratio to 9 percent.
The private sector must take up at least 10 percent of the new shares to be issued to keep lenders privately run.
Alpha said its total recapitalisation need, as set by the central bank, was 4.6 billion euros. NBG said its capital need was 9.7 billion.
Greece's two other big lenders, Eurobank and Piraeus, unveiled their recapitalisation needs on Thursday, set by the central bank at 5.8 billion euros and 7.3 billion respectively.
This means the total recapitalisation need for country's four systemically important banks comes to nearly 28 billion euros.
Banks will have to complete their capital raising under the plan by end-April next year. (Editing by David Holmes)