The European Central Bank is set to hold emergency talks on whether to continue its financial lifeline to Athens, with France warning of a "real risk" of a Greek exit from the euro.

After talks in Brussels broke down in acrimony on Saturday between Greece's left-wing leaders and the rest of the eurozone, Greece hurtled toward default with its EU-IMF creditors, left solely reliant on emergency cash from the ECB.

Anxious Greek citizens queued at cash machines fearing that capital controls may be introduced and the scenario of a Greek exit from the euro is expected to unsettle global financial markets on Monday morning.

Hopes were slim that ECB chief Mario Draghi and the Governing Board, who were set to hold a telephone conference, would keep cash-starved Greece on financial life support, which was so far based on hopes Greece would reach a deal.

A source close to the negotiations on Saturday said there was "no reason to give more money".

"The ECB will suspend ELA tomorrow, it's clear," the source said, referring to the so-called Emergency Liquidity Assistance.

French Prime Minister Manuel Valls warned of a "real risk" of Greece leaving the eurozone if the Greek people voted against the EU's bailout proposals in a referendum next weekend.

Voicing hopes that a "deal is still possible" with Athens, he said of the independent ECB: "I don't think they can cut off the lifeline. It's the Greek people who are suffering."

Draghi has insisted that solving the Greek crisis is up to politicians, not central bankers, and faces EU rules that bar the ECB from directly financing a eurozone government.

For the past five months of negotiations, the Frankfurt-based ECB has kept alive Greek banks and the state.

Everything changed on Saturday after Greek Prime Minister Alexis Tsipras stunned Europe with a surprise call for a July 5 referendum on the latest cash-for-reforms package and passionately advised voters against backing a deal that spelled further "humiliation".

Late on Saturday, Greek parliamentarians voted in favour of the referendum. Tsipras told the parliament he was confident "the Greek people will say an emphatic no to the ultimatum" by EU-IMF creditors, but "a big yes to European solidarity".

Exasperated eurozone members refused to extend the EU's critical financial lifeline beyond a Tuesday deadline, freezing the final tranche of bailout cash.

This will almost certainly mean Greece will default on more than 1.5 billion euros owed to the International Monetary Fund on Tuesday.

IMF chief Christine Lagarde said the Washington-based fund would also close off the money tap in response to what would be the first ever default by an advanced economy.

Lagarde, speaking to the BBC overnight, voiced the slimmest of hopes that disaster could be averted, quoting German Chancellor Angela Merkel, who has repeated, mantra-like, that "where there's a will, there's a way".

Lagarde pointed out that, given that EU lending would have stopped, "at least legally speaking, the referendum will relate to proposals and arrangements that are no longer valid".