World markets have tumbled as Greece shut its banks and imposed capital controls to halt a panic-driven run on ATMs, a day before Athens risked defaulting and possibly crashing out of the euro.

But in a narrow ray of hope, creditors left the door open for a last-ditch debt deal to try and avert a Greek eurozone exit which would raise serious questions about the future of the EU.

Calling for a compromise, German Chancellor Angela Merkel warned that "if euro fails, Europe fails".

Global stocks fell, with Frankfurt and Paris losing more than three per cent after a slump in Asia. The euro steadied after hitting a one-month low under $1.10 on Sunday.

Athens issued a decree to close banks until July 6 - the day after a referendum on creditors' bailout proposals - with a 60 euro ($A86.65) limit on ATM withdrawals.

Foreign tourists, a vital engine of the Greek economy, will be exempt.

However, the drastic measures - designed to protect the banking system against the threat of mass panic - sent Greeks rushing to withdraw their daily allowance.

Jittery housewives, shoppers and business owners formed long lines at cash machines across Greece on a day dubbed "Black Monday".

"No money, no hope, how did we get in this situation? This is Black Monday," unemployed Chris Bakas, 28, said as he stood sweating in the Athens sun, staring at an ATM screen.

Prime Minister Alexis Tsipras had urged restraint on Sunday after announcing the restrictions.

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

The Athens stock market has meanwhile been shut until July 7.

The rapid escalation of the Greek debt crisis came after the European Central Bank froze the level of its emergency lifeline for Athens on Sunday, despite a growing bank run.

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

In reaction, eurozone finance ministers angrily rejected a request to extend the bailout beyond its expiry on Tuesday, sparking fears Greece could default on a key IMF loan repayment due the same day - and potentially crash out of the eurozone eventually.

EU commissioner of economic affairs, Pierre Moscovici of France, declared Monday that "the door is always open to negotiations" for Greece, adding negotiators had been "a few centimetres" from a deal when talks collapsed.

The Commission - one of the "troika" of creditors along with the ECB and the International Monetary Fund - said temporary restrictions on the free movement of capital were "justified ... to maintain financial stability".

The Frankfurt-based ECB's governing council on Sunday and left unchanged its 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 in Greece's festering debt crisis after five months of tough bailout talks culminated on Friday night with Tsipras's shock call for a referendum.

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 ($A2.17 billion) due to the IMF that same day.

In Berlin, Merkel is still prepared to hold talks with Greek Prime Minister Alexis Tsipras despite the breakdown in debt negotiations at the weekend, her spokesman said.

French President Francois Hollande added that Paris was "always available" for negotiations with Athens -- and that a bailout deal remained possible.