Big banks and pension funds have thrown their weight behind the attempt to avoid a messy Greek default as holders of €81m (£75m) of the country's bonds said they will participate in the debt relief programme.
The 39% support for the debt swap deal came ahead of today's 8pm deadline and after a warning from the Institute of International Finance which said that a disorderly default would cost at least €1trn.
Private investors exposed to Greek debt will swap their bonds for new ones but face an overall loss of 75% on their holdings as well as longer repayment times and lower interest rates.
Greece, under the stewardship of technocrat leader Lucas Papademos, claims that despite the losses the cut represents a good deal for investors as the alternative is to go empty-handed if the country could not secure the €130bn (£108bn) in bailout loans from the EU/IMF/ECB troika.
Investors hold €206bn (£172bn) in Greek bonds.
Under the rules, Greece needs to secure a participation rate of over 66% but for some of the bonds the rate must be higher. A rate of more than 75% but less than 90% is seen as the most likely by analysts.
A successful bond swap is crucial if Greece is to get its second €130bn (£108bn) loan, one which would stop it from becoming the first eurozone country to default when a €14.5bn (€12bn) bond redemption becomes due.
News of progress towards a deal helped boost stock markets around the world yesterday with the Dow Jones Industrial Average rallying close to 100 points.
Markets also warmed to reports the US Federal Reserve is looking at implementing further stimulus to boost economic activity in the US. The Wall Street Journal reported that Fed officials are considering buying back long-dated bonds, a move which will inject cash into the economy.