The buyback is designed to provide for about half of a 40-billion euro debt relief package for Athens agreed last month by the European Union and International Monetary Fund.

Its success is crucial to ensuring Greece's debt is put back on sustainable footing and -- more immediately -- to unlocking badly-needed aid for the country.

The offer had been due to end on Friday. The debt agency extended the offer to 7 a.m. EDT on Tuesday.

"The aim is to reach the 30 billion euro target on the face value of debt to be bought back," said a government official, who declined to be named.

Greece was given 10 billion euros to conduct the buyback. They source said the aim was to use all of it.

A senior Greek banker who spoke on condition of anonymity said Athens aimed to use the delay to get another 3 to 4 billion euros worth of bonds offered for exchange.

"This will be easily covered by Greek banks, if foreign bondholders do not offer more," the banker told Reuters.

Greek banks and insurers had tendered about 10 billion euros of bonds out of their total holdings of about 17 billion euros, the banker said. Nearly 63 billion euros of Greek debt held by private investors was eligible for the buyback.

Shortly before the previous Friday deadline expired, Greek banks got board approvals to offer as much as 100 percent of their bondholdings to make the buyback work.

Athens had offered better-than-expected terms for the buyback to entice investors, with price ranges at a premium over market prices.

But Greek lenders had been reluctant to sell back to the government all of their bondholdings, trying to limit the future profits and interest income on their bonds they will forego.

However, they are expected to assist to ensure a successful buyback since they depend on the bailout funds that Athens stands to receive once it is completed. A big chunk of the 34.4 billion euros of aid due will be used to recapitalize them.

Athens badly needs the aid to revive its ailing economy, which is on track for a sixth year of recession due to austerity measures including spending cuts and tax hikes.

The EU and the IMF have been withholding rescue payments to Greece for six months because it had failed on pledges to shore up its finances, privatize and make its economy more competitive.

Greece and its international lenders had shied away from setting a binding target for the buyback, apart from saying that Athens would spend a maximum of 10 billion euros on it.

Under the scheme, Greece was expected to spend that amount to repurchase 30 billion euros of debt, shaving it by a net 20 billion euros. That would help slash Greece's debt to 124 percent of GDP by 2020, ensuring that the IMF stays on board in the country's rescue.

Greece set December 18 as the settlement date for offers on the 20 series of outstanding bonds it is buying back.

(Writing by George Georgiopoulos,; Editing by Deepa Babington/Jeremy Gaunt)

• A Permanent Economic Emergency