Greece has announced that it will shut banks for a week, pleading for calm after anxious citizens emptied cash machines in a dramatic escalation of the country's debt crisis.

Banks will be closed until July 6 inclusive - the day after a referendum on bailout proposals - with a 60 euro limit on ATM withdrawals, but foreign tourists, a vital engine of the Greek economy, will be exempt from the restrictions.

The drastic measures to protect Greece's banking system against the threat of mass panic came after the European Central Bank said it would not increase its financial support to Greek lenders, despite early signs of a chaotic bank run.

It capped a weekend of high drama that began with Prime Minister Alexis Tsipras's unexpected call for a July 5 referendum on creditors' latest reform proposals after bailout talks in Brussels collapsed.

In response, angry EU and IMF creditors rejected a request to extend the nation's bailout beyond its June 30 expiry date, sparking fears Greece could default on a key debt payment to the IMF due the same day and possibly crash out of the eurozone.

Uncertainty over how events will unfold in coming days prompted crowds to form long queues outside some ATMs in Greece, leaving many cash machines dry.

Keen to stave off panic, Tsipras assured Greeks their deposits were "totally safe".

"Any difficulties that may arise must be dealt with calmness. The more calm we are, the sooner we will get over this situation," he said, adding that Athens had again requested a "prolongation of the (bailout) program".

With the Athens stock exchange closed Monday, other global markets were expected to follow Asia's lead in what is set to be a highly volatile day of trade as investors return to their desks to find Greece hurtling towards default.

The Frankfurt-based ECB's governing council held a crisis telephone conference on Sunday and pledged to maintain emergency liquidity assistance - keeping open its life support for Greek banks and, by extension, the Greek state. But it pledged no extra cash for banks.

The move further raised the stakes after five months of tough bailout talks culminated on Friday night with Tsipras's shock call for a referendum on the creditors' latest cash-for-reforms offer.

Unless creditors heed Tsipras's renewed request for a bailout extension, Greece's rescue plan will formally expire on Tuesday. This will almost certainly mean Greece will default on more than 1.5 billion euros due to the IMF that same day.

Greek Finance Minister Yanis Varoufakis said there was still time for a compromise, urging creditors to show some "goodwill" and come up with an improved proposal ahead of the plebiscite.

We remain open to new proposals by the (creditor) institutions," he told the German daily Bild.

A banking source in Greece said only 40% of cash machines now had money in them.

Since Friday night alone, 1.3 billion euros have been withdrawn from the Greek banking system, according to the head of the bank workers' union Stavros Koukos.

Tsipras, whose Syriza party came to power in January on an anti-austerity platform, has advised voters against backing a deal he said spelled further "humiliation" for a country that has endured five years of recession, turmoil and skyrocketing unemployment.