But teller Costas Alafouzos says a steady stream of customers have been taking out their money as expectations have grown that Greece could be facing a decisive turning point after a crisis that has lasted more than five years.

"You don't see it, there are no lines but it's happening. There has been a rise in withdrawals, mostly in cash this last week," he said.

As the standoff between the government of leftist Prime Minister Alexis Tsipras and its creditors in the European Union and International Monetary Fund has deepened, there have been growing warnings of an "accident" that could force Greece out of the euro.

This is what it may look like.

If the pace of withdrawals continues, Greece may have to introduce capital controls, limiting the amount people can take out of their bank accounts and bringing into plain sight the prospect of an exit from the euro that would ravage savings.

"It's very possible that this thing we hope to avoid will occur. Of course if it happens, the next step is chaos and catastrophe," said 55-year-old economist Ioannis Simaresis as he queued up to take money out of a cash machine.

For months, Greek banks have relied on emergency infusions of central bank funds to stay afloat, but with more than 4 billion euros taken out of the system this week, reserves are shrinking fast.

If the withdrawals continue, a credit system that has been hollowed out during years of recession could reach the point of no return.

The starkest warning came on Thursday from ECB Executive Board member Benoit Coeure, who told euro zone finance ministers that he was not sure if the banks would be able to open on Monday, according to participants at the meeting.

A crisis meeting of the ECB Governing Council on Friday decided to increase the amount of emergency finding available to the banks - but not by enough to keep the system going for long if no political solution to the crisis is agreed.

With corporate and household deposit outflows totalling more than 30 billion euros between October and April, balances are at their lowest level in more than a decade, paradoxically leaving the economy awash with cash.

Banknotes in circulation, part of what economists call the M0 money supply indicator, rose to 43.5 billion euros in April from just over 30 billion in November - showing that about a quarter of what Greece's economy produces annually is floating around in the form of physical currency.

SLOWDOWN

Cash levels that high underscore how far the banks' role as the heart of the economy pumping finance to households and business has been weakened during the crisis.

For months, Greek banks have been in slowdown mode as lending activity has dried up while the government has wrangled over a new package of funding from its lenders that it needs to stave off default.

The huge load of bad and doubtful loans the banks are saddled with has limited their ability to extend credit to an economy that has fallen back into recession, while a gradual return of deposits seen towards the end of last year has reversed and interbank access has frozen again.

"A large part of our operational energy is devoted to containment, dealing with liquidity pressures and problem loans," said one banker, who spoke on condition of anonymity because he is not authorised to speak to the press.

Greece's retailers' association says about 95 percent of businesses' applications for loans are being rejected by commercial banks. Many small and medium-sized firms have stopped even asking banks for credit.

With interest rates at rock bottom and an economy in deflation for more than two years, the only reason to keep money in the bank is security and convenience.

"The potential upside, if the situation normalises, is that people will bring this money back to the banks. This will improve deposit balances, they will not want to keep holding it in cash," said another banker.

That reflects the steps that many Greeks have already taken to ensure their cash is not trapped in the bank, following a previous banking scare in 2012, when Greece came close to leaving the euro and savers took fright.

As a result, there is none of the panic seen for instance when Britain's Northern Rock bank ran into trouble in 2007, with long lines of worried and angry depositors queueing up outside its branches.

The richest Greeks are believed to have taken the bulk of their fortunes abroad long ago but even small savers have made their preparations.

"Personally, I have already taken precautionary measures," said Daphne Alexiou, a 66-year-old pensioner, who was withdrawing just a small amount of cash ahead of the weekend.

(Additional reporting by Gina Kalovyrna, Writing by James Mackenzie; editing by David Stamp)

By George Georgiopoulos