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* Deadline for offers expired at 1200 GMT
* Greek banks put up most of holdings - bankers
By George Georgiopoulos and Lefteris Papadimas
ATHENS, Dec 11 (Reuters) - Greek banks are expected to have tendered most or all of their Greek sovereign debt by Tuesday's deadline, bankers said, suggesting Athens has hit targets under the bond buyback scheme needed to cut debt and unlock aid.
Athens gave bondholders until 1200 GMT on Tuesday to tender Greek debt under the scheme after the amount offered by Friday's initial deadline fell short of the targeted 30 billion euros.
The cut-price buyback's success is crucial to putting Greece's debt back on a sustainable footing, which in turn allows lenders to disburse aid to Athens.
Greek banks, who had only tendered about 60 percent of their roughly 17 billion euros in sovereign debt holdings by Friday, offered all or most of their holdings to ensure the buyback hits its targets, senior banking executives told Reuters.
"Greek banks have contributed almost all of the bonds they had left," a senior bank executive said minutes after the 1200 GMT deadline passed, adding Athens had probably got offers for as much as 31.5 billion euros.
That is well above the 26.5 billion euros that a senior euro zone official told Reuters had been tendered as of Friday, at an average price of 33.4 percent of face value.
A second banker said his bank had offered the rest of its sovereign debt, and that other Greek banks had tendered all their holdings, so that Athens was offered an additional 4.5 to 5 billion euros in debt.
A third banker also estimated total offers represented debt worth about 31 billion euros.
"Banks tendered more bonds, the biggest part of their holdings," said the banker.
Euro zone finance ministers are expected to discuss the outcome of the buyback in a teleconference later on Tuesday.
Greek lenders had initially been reluctant to put up their entire holdings, fearing losses over the long term, but now have little choice but to do more since most of the aid unlocked by a successful buyback will go to boosting the lenders themselves.
The buyback scheme calls for Greece to buy back debt worth 30 billion euros using 10 billion euros from foreign lenders at prices well below their nominal value, cutting debt by a net 20 billion euros. That would account for half of a broader debt relief package lenders agreed for Athens last month.
If the debt tendered exceeded the 30 billion euro target, the debt agency may end up accepting the additional amount, said a Greek government official who declined to be named.
"They will decide after the books are closed," the official said.
Athens had set a price range for the buyback at a premium to market prices at the time. The range varied from a minimum of 30.2 to 38.1 percent and a maximum of 32.2 to 40.1 percent of the principal, depending on the maturities of the 20 series of outstanding bonds.
Hedge funds, which bought the debt at rock-bottom prices when it was feared the country would exit the euro, are estimated to hold a large part of Greek debt and the offer was seen as likely to earn them a tidy profit.