As Athens scrambles to meet the conditions for more bailout funds, alarm is also mounting about European banks that have lent Greece and other debt-strapped nations hundreds of billions of dollars. Some of the biggest lenders are located in Europe's two biggest economies: Germany and France.
Pushing a stroller on a weekday afternoon, 29-year-old Lucas Sulej ran an ordinary errand: he took out money at a bank machine in eastern Paris. But these days Sulej no longer takes his French bank, Societe Generale, for granted - not since Moody's cut its rating last week, partly because of its large exposure to Greek debt.
"I have money in Societe Generale and maybe tomorrow it may disappear. Because you know the problems of Societe Generale," said Sulej.
Analysts say banking insurance and governments will protect ordinary European savers like Sulej. But the young father is not the only one concerned about the health of Societe Generale and other European banks which have lent hundreds of billions of dollars to debt-strapped governments like Greece.
At issue, says Thomas Klau, head of the Paris office of the European Council on Foreign Relations, is not the downgrading of banks like Societe Generale - which overall still has a good credit rating.
"The trouble is that the loss of confidence within the financial markets - but also within the core parts of the financial industry themselves - has now reached such proportions that any negative move can have extremely bad consequences," he said.
Analysts say part of the problem is a lack of transparency within Europe's banking sector and that is deepening the alarm in the markets. Simon Tilford is chief economist at the London-based Center for European Reform.
"They don't know which banks are sitting on which debt, so they are becoming increasingly loathe to loan to European banks," said Simon Tilford, chief economist at the London-based Center for European Reform.
In a move to restore market confidence, major central banks around the globe agreed last week to inject dollars into Europe's banking system to fight fears it is running short of cash. But Tilford says the move is not enough.
"All it does really is provide liquidity and that's useful, but the underlying problem is essentially a solvency one, in that there is an awful lot of debt that's going to get written off in Europe and that is going to impose very, very considerable losses on financial institutions," he said.
In other words, if Greek or other ailing European economies default, a number of European banks may be left with enormous amounts of unpaid debt. Experts say some may ultimately go under.
Europe's banking crisis has been compared to the one faced in the United States in 2008, after U.S. investment bank Lehman Brothers collapsed. Analysts say the consequences both then and now are global. Underscoring American concern about Europe's sovereign debt and banking problems, U.S. Treasury Secretary Timothy Geithner made a rare appearance at a European finance ministers meeting on Friday.
"A full-blown financial crisis in Europe would not be contained in Europe. This would spread immediately to the U.S. Much as the financial crisis in the U.S. spread to Europe - it would be a similar move, but in the opposite direction," he said.
Adrian Blundell-Wignall, special financial markets advisor for the secretary general of the Organization for Economic Cooperation and Development, says U.S. authorities moved swiftly and forcefully to tackle their own banking crisis three years ago - and to acknowledge the size of the problem. He contrasts this with Europe's response today.
"I think that the biggest part of that difference has to do with transparency," he said. "Transparency is really good. Sunlight is a great disinfectant and it brings everybody together. People know what they have to do, market participants know what they have to do."
A case in point, analysts say, are stress tests on European banks, which aren't considered tough enough. Only nine banks failed the tests this year. Those results helped undermine investors' confidence in the banking system.
Because many banks in France and elsewhere do business across Europe, analysts like Klau, of the European Council, believe there must be a European solution to the banking crisis.
"We desperately need a eurozone or a European approach guaranteeing deposits in the banks and doing that jointly. And Europeanizing the potential rescue of banks that come under massive pressure, either as the result of the ongoing loss of confidence or as a result of future developments which might make the crisis even worse than it is," he said.
But that means European governments must invest in a much deeper financial integration than they have been willing to accept so far. Indeed, criticism is rising in richer countries like Germany - whose banks hold a sizable amount of Greek debt - about having to bail out poorer ones like Greece.
Former IMF chief Dominique Strauss-Kahn is among many experts who say European nations haven't faced up to reality.
Speaking on French television Sunday night, Strauss-Kahn said Europe's governments and banks must realize they will have to take a loss when it comes to Greece and possibly other struggling European economies. But instead of tackling the problem, he says, governments are just pushing it off - so that it grows even larger.