A group of 30 banks and funds representing 40.8 percent of Greece's 206 billion euros of outstanding debt said they would take part in the deal, joining other Greek and foreign banks and pension funds which have already pledged to accept the offer.

A senior Greek finance ministry official told Reuters the government was now optimistic that well over 75 percent of eligible bonds would be submitted, easily clearing the original minimum threshold it had set for the deal to proceed.

In total, bank, insurers and pension funds holding bonds worth around 120 billion euros have already declared they will take part.

Athens, totally reliant on international support to stave off bankruptcy, has asked its private sector creditors to accept steep losses on their Greek bond holdings as it fights to cut a public debt burden of 160 percent of gross domestic product.

They are being asked to give up almost three quarters of the value of their investments in return for new Greek bonds. If they do not accept the offer, Greece has threatened to pay them nothing.

The European Union and International Monetary Fund have made a successful bond swap a pre-condition for final approval of the 130 billion euro ($170 billion) bailout agreed last month.

With just over a day to go before the offer expires, the latest commitments bring the declared total closer to the two thirds minimum level needed for Greece to enforce losses on any holdouts, ensuring the deal goes through.

Amid signs that acceptances had picked up strongly on Wednesday, a string of international banks and insurers, ranging from Germany's Munich Re to Bank of Cyprus declared they would back the deal.

But after months of tortuous negotiations and repeated setbacks, senior bankers and officials remained cautious ahead of the deadline.

"About the private sector deal - I don't have a crystal ball. I cannot predict this with certainty. But I repeat, for us, this is a condition," Dutch Finance Minister Jan Kees de Jager told parliament.

Only 177 billion euros of the debt are covered by Greek law and it was not immediately clear how much of the debt covered by Wednesday's commitment was under Greek law and how much under international law.

Athens only has the power to enforce losses on holders of bonds written under Greek law, not the 10 percent or so of its debt covered by English or other international law.

"It is impossible to be certain of the outcome of such a process," French bank BNP Paribas' Greek debt negotiator Jean Lemierre told Le Monde newspaper. "But the success of the offer is in everyone's interest."

JITTERY

Financial markets have become more jittery the closer the Greek bond deadline has got and worries about the bond swap lifted demand for German bonds on Wednesday, as investors sought a safe haven for their money before the deadline.

Greece, unable to borrow normally on the bond markets, urgently needs the bailout to keep paying its bills while it attempts to make deep structural reforms to its shattered economy, now in the fifth year of deep recession.

Euro zone finance ministers are due to decide whether to release the 130 billion euros package during a conference call on Friday but they have already approved the bailout, subject to the private sector creditor agreement.

Athens, which has annoyed its international partners by repeatedly missing reform targets, must have the funds cleared by March 20, when redemption payments on 14.5 billion euros of bonds fall due.

Greece has staggered from one deadline to another since the euro zone crisis blew up in 2010 and even if the bailout is passed, several international partners have said more support will be needed before long.

Although the Greek economy is small in international terms, a disorderly default could severely destabilize the euro zone and create a banking crisis that many analysts fear could surpass the Lehman Brothers disaster of 2008.

Underlining the problems facing the economy, the head of SETE, the association representing Greece's vital tourism sector, said pre-bookings from key markets including Germany and the Netherlands were down by 20-30 percent this year.

Following repeated waves of strikes and sometimes violent protests in Athens and other big cities, Greeks have become increasingly disillusioned with politicians ahead of elections expected by early May at the latest.

On Wednesday, prison guards kicked off a series of 24 hour rolling strikes in protest against worsening conditions in the country's already severely overcrowded prisons. Greeks also booed and threw yogurt at politicians during a parade on the island of Rhodes. ($1 = 0.7625 euros)

(Writing By James Mackenzie, editing by Mike Peacock)

By Lefteris Papadimas