(Corrects share of Greek operations as total of Popular Bank, 8th paragraph)
ATHENS, March 16 (Reuters) - Cypriot banks will transfer their Greek units to Greek owners as part of the island's international bailout agreed earlier on Saturday, two government and banking sources in Athens told Reuters.
Cypriot banks account for the bulk of the 10 billion euros ($13 billion)that Nicosia will get from euro zone countries to stave off bankruptcy. In sharp contrast with previous bailouts for other indebted nations, the rescue package is co-funded by levies on bank deposits.
The units of Cypriot banks in Greece, which account for about a tenth of Greece's banking market, were specifically excluded from the levy after a deal to transfer them to Greek lenders, one senior banking source and one senior finance ministry official said.
"They will be transferred to a Greek bank," the finance ministry official said. It was not yet clear which Greek bank would take them over and on what terms.
Greek lenders have themselves been bailed out with up to 50 billion euros in EU/IMF funds after a Greek debt cut in 2012 severely hit the value of their bondholdings.
The eurogroup said earlier on Saturday, without elaborating, that it welcomed "that an agreement could be reached on the Greek branches of the Cypriot banks, which protects the stability of both the Greek and the Cypriot banking systems".
It said this would be done in a way which "does not burden the Greek debt-to-GDP ratio".
Cyprus's two top lenders with a presence in Greece are Bank of Cyprus and Popular Bank. Greek operations accounted for more than a quarter of total group operating income at Bank of Cyprus and 10 percent at Popular, according to nine-month 2012 results.
According to Greek media reports, Cypriot lenders' assets will be most likely transferred to Hellenic Postbank, a formerly state-controlled lender which was itself bailed out in January.
But a Postbank official told Reuters it was not yet known if this would happen.
Postbank, whose capital shortfall was estimated at 3.7 billion euros, passed into the full ownership of Greece's bank bailout fund (HFSF) with a view to being sold at some point to private investors. ($1 = 0.7654 euros) (Reporting by Harry Papachristou, Editing by Mark Trevelyan)