Athens gave bondholders until 7 a.m. EDT on Tuesday to tender Greek debt 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, are expected to offer more to ensure the buyback hits its targets, senior banking executives told Reuters.

"All banks will support the buyback, topping up their offers," said one banker at a major Greek bank, who declined to be named. "The target of 30 billion euros will be reached and may be exceeded."

A total of 26.5 billion euros was tendered at an average price of 33.4 percent of face value by the close of play on Friday, a senior euro zone official told Reuters.

Euro zone finance ministers are also expected to discuss the outcome of the bond buyback in a teleconference late on Tuesday afternoon, after the extended deadline expires.

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.

A second banker also said Greek lenders would have tendered most of their bondholdings by Tuesday's deadline, which could push the bids Athens receives over the 30 billion euros target.

"Banks will tender a significant amount of their bondholdings in the buyback," that banker said.

"They will end up with small amounts left over in their portfolios. The total amount offered in the buyback invitation may reach 31-32 billion euros."

The buyback scheme calls for Greece to buy back debt worth 30 billion euros with 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.

(Writing by Deepa Babington, editing by Mike Peacock)

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