A summit of the 17-nation euro group was proposed by European Council president Herman van Rompuy in Brussels to prevent larger euro zone economies such as Italy and Spain from being sucked into the crisis by demonstrating their determination to help keep Greece from defaulting on its debts.
However, the differences over involving the private sector in the proposed second bailout package of up to 120 billion euros were so great that they decided to delay their meeting until next week.
The euro zone's largest economy, Germany, which has been pressing for involvement of the private sector to share the costs of a future financial rescue of Greece, saw no urgency in convening a summit of the heads of state and government as long as they are not in a position to take a decision.
If they continued to squabble over the terms of a second financial rescue of Greece a year after it received a bailout of 110 billion euros (159 billion dollars), they will be sending a wrong signal to financial markets, Germany argued.
A prerequisite for an emergency summit is that "we can agree on a complete, new programme for Greece", Chancellor Angela Merkel said on Thursday in Nigeria, where she concluded a three-nation African tour.
Some of Germany's partners as well as the European Central Bank have been opposing any solution that will be seen by financial markets as a partial default by Greece.
Italy and Spain have been demanding speedy action by their euro zone partners on a new rescue package for Greece because they are already being targeted by speculators as the next candidates for a bail-out after Greece, Ireland and Portugal.
Borrowing costs for Italy and Spain soared to record levels at the beginning of this week and they fear that if the uncertainty about the second bailout package continued, it will become more difficult for them to raise funds in the financial markets and the debt crisis will engulf the entire euro area.
The second rescue package is intended to give Greece more time to pay back its debts, which grew to a staggering 350 billion euros even after it received the first bailout in May last year.
Two weeks ago, the euro zone nations released the fifth tranche of 12 billion euros from last year's rescue package immediately after the Greek Parliament endorsed a new package of tough austerity measures.
It prevented Greece from defaulting on its debt repayments due this month and ensures that it will remain solvent until September.
Italy's success in raising 2.97 billion euros from financial markets on Thursday, even though at a very high interest rates, showed that the country is still a far cry away from the situation in Greece, which was forced to seek a bail-out in May last year.
However, Italy had to offer a record 5.9 per cent yield on 15-year bonds and 4.9 per cent yield on five-year bonds.
The Italian senate's approval on Thursday of a 48 billion euro austerity plan over three years is expected to calm down the financial markets, which became jittery in the past few days over fears of the Greek debt crisis spilling over to Italy and Spain.