Eurozone finance ministers have rejected a Greek request to extend a bailout programme beyond 30 June.
A Eurogroup statement said Greece had broken off negotiations over a new bailout deal "unilaterally".
Late on Friday, Greek PM Alexis Tsipras called a surprise referendum for 5 July over the terms of any new deal.
Greece has to pay €1.6bn (£1.1bn) to the IMF on 30 June. Without new funds, there are fears Greece may leave the euro and its economy may collapse.
Greek Finance Minister Yanis Varoufakis said Greece would still try to secure a bailout deal that could then be put to a referendum.
"In these crucial moments, the Greek government is fighting for there to be a last-minute deal by Tuesday," he said.
The Greek parliament is due to vote later on whether to ratify the referendum.
Addressing MPs just before the vote, Mr Tsipras urged the Greek people to say a "resounding 'no' to ultimatums" by creditors.
Eurogroup head Jeroen Dijsselbloem said it would be up to the European Central Bank (ECB) to decide whether to continue providing emergency liquidity funding to the Greek banking system.
In Greece, queues have formed outside banks amid concerns that the Greek central bank might start restricting withdrawals.
Analysis: Chris Morris, BBC News, Brussels
It's never over till it's over. But it feels like the end is perilously close. The breakdown in talks between Greece and its creditors has to be seen as a failure.
It wasn't supposed to happen like this. It is also a massive gamble on all sides, and a possible turning point in the history of the eurozone. There will still be those working feverishly behind the scenes for compromise, but in effect neither side has blinked yet.
When the Greek government thought it had made substantial concessions at the beginning of the week, the creditors said it simply wasn't enough. And while no-one can say for certain that Greece will leave the eurozone, this is already uncharted territory.
Much will depend on the outcome of the referendum called by PM Alexis Tsipras, if it takes place on schedule. And much will also depend on the European Central Bank - and whether it believes it can still allow funds to flow, to prevent banks in Greece from collapsing.
The head of the International Monetary Fund, Christine Lagarde, told the BBC that because the European part of Greece's bailout programme would have expired by 5 July, any referendum would relate to "proposals and arrangements which are no longer valid".
But she said that if there was a "resounding 'yes'" to staying in the eurozone, then the response would be "a resounding 'let us try'".
Mr Dijsselbloem said the Eurogroup would continue to work with Greece and that many scenarios were conceivable.
But he placed the blame squarely with Greece for walking out of negotiations on Friday.
"They broke off their talks while they were still going on, while there was still time," he said.
"The only positive caveat I see is that the Greek parliament still has to take a wise position on that, and I hope that may lead to a different political situation."
French Finance Minister Michel Sapin stressed that all the Eurogroup's members wanted Greece to remain in the eurozone.
"This is not a Greek exit from the eurozone," he said after crisis talks between the Eurogroup and Mr Varoufakis on Saturday. "The 18 countries, apart from Greece, all said clearly that Greece was in the euro and should remain in the euro whatever the difficulties of the moment."
At the scene: Joe Miller, BBC News, Athens
Throughout the ups and downs of the recent negotiations, Greeks have by and large resisted the urge to withdraw money from their accounts, pinning their hopes on a last minute deal with the country's creditors.
But as the deadline for Greece's €1.6bn payment to the IMF looms, and with Mr Tsipras calling for a referendum next week, lines have begun to form outside ATMs and bank branches in Athens.
One bank has imposed withdrawal limits of €3,000 per account, and some ATMs have handwritten "empty" signs on them - although I managed to withdraw cash at two separate locations.
Some customers were given a ticket number and told to come back in a few hours. One man told me he was 170th in line. "The game is over," said Peter, one of those queuing. "Greece is going into uncharted waters, and the banks will be closed on Monday, I suspect."
Anxiety is mounting in Athens. "Everybody's really scared," Elena, a woman in her 20s, tells me as she waits to withdraw cash. "We need to have enough money to last the week."
Mr Varoufakis told reporters that the Eurogroup's refusal to extend the bailout could permanently damage the credibility of the group.
He said that what had been proposed to Greece "did not contain any plan for giving, instilling hope in investors, both Greek and non-Greek, in consumers, in depositors".
He said his government had asked for an extension of "a few days, a couple of weeks", whereas Mr Dijsselbloem said an extension of one month had been requested.
Greece owes roughly €340bn, mostly to its eurozone partners. Because it can no longer borrow from the international money markets, it is dependent on the eurozone and IMF to keep its banks functioning.
Greece timeline: Key dates ahead
- 27 June: Eurogroup refuses Greek request to extend existing bailout
- 30 June: Troika bailout programme ends as Greek €1.6bn payment to IMF due
- 1 July: No bailout programme could mean no emergency liquidity from the ECB
- 5 July: Proposed Greek referendum
- 10 July: Treasury bills worth €2bn to be repaid
- 20 July: Bonds worth €3.5bn to be repaid to eurozone partners
- 20 August: Bonds worth €3.2bn to be repaid