French President Nicolas Sarkozy has said allowing Greece into the eurozone in 2001 was a "mistake".
He said Greece was "not ready" at the time. But, he added, it could be rescued thanks to Wednesday's EU deal on the euro debt crisisIn response, Greece's foreign minister told the BBC that Athens was not the source of the crisis, and that no country should be made a scapegoat.
The agreement reached in Brussels has triggered a worldwide shares rally.
In a TV interview on Thursday, Mr Sarkozy said admitting Greece to the eurozone had been "a mistake" because the country had "entered with false [economic] figures. It was not ready".
He added that he was confident the current Greek government would emerge from the crisis and that Wednesday's deal had averted a "catastrophe".
"If Greece had defaulted, there would have been a domino effect carrying everyone away," Mr Sarkozy said.
Speaking to the BBC, Greek Foreign Minister Stavros Lambrinidis said: "Greece is in the middle of the storm, but it is not the source of the problems of European debt and deficits.
"We see this with Portugal, Ireland, Spain and Italy. So it doesn't help to scapegoat a particular country when you're dealing with a European problem."
The comments come after European leaders clinched a deal at marathon talks in Brussels. The main provisions are:
The agreement is aimed at preventing the crisis from spreading to larger eurozone economies, but the leaders said work still needed to be done.
BBC business editor Robert Peston says EU leaders have bought some time, and the markets will give them the benefit of the doubt for a few weeks or months.On Friday, Klaus Regling, chief executive of the EFSF, held talks in Beijing, as the eurozone bloc continued its efforts to persuade China - and other emerging economies - to help rescue it from its crippling debt crisis.
Analysts say that a possible Chinese investment could be up to $100bn, the BBC's Martin Patience in Beijing reports.
But China is seeking guarantees from Europe that its investments will be safe, our correspondent adds.
Super-commissioner Hailing Wednesday's deal, European Commission President Manuel Barroso said: "Europe is closer to resolving its financial and economic crisis and to getting back on a path of growth. We are showing that we can unite in the most difficult of times."
He said the post of "super-commissioner" would be created to deal with the euro.
US markets joined Europe's share rally. The Dow Jones index ended the day up 2.86%.
London's 100 share index finished up 2.9%, France's Cac up 6% and Germany's Dax 5% higher.
The biggest gainers were banks, led by French institutions, which are the most exposed to Greek debt.
Fears about the state of the eurozone's finances and the threat of a break-up of the single European currency have been stalking markets for months.
The 50% debt write-off by banks means that Greece's debt burden could drop from 160% of GDP to 120% by 2020.
Eurozone leaders said the firepower of the EFSF would be boosted from the current 440bn euros to about 1tn euros - although details remain to be worked out.
The framework for the new fund is to be put in place in November. Germany, as the largest economy in eurozone, is expected to be the largest contributor.
Bank recapitalisation was agreed earlier.
The banks will now be required to raise about 106bn euros in new capital by June 2012, and governments may have to step in, despite the unpopularity of further bank bail-outs.
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