The International Monetary Fund has confirmed Greece had not made its €1.5bn loan repayment to the Fund, making it the first advanced economy to ever be in arrears to the Fund.
The missed payment, the largest in the Fund's history, is equivalent to a default, in that both imply a breach of Athens' obligations.
IMF spokesman Gerry Rice said Greece can now only receive further IMF funding once the arrears are cleared.
Rice confirmed that Greece had asked for a last-minute repayment extension earlier on Tuesday, which the Fund's board will consider "in due course."
Earlier, the chairman of the Eurogroup said Greece was on track to default at midnight and Athens' stance towards its creditors would have to change before its euro zone partners could consider any additional financial assistance.
Speaking after an emergency conference call between the currency bloc's finance ministers, Jeroen Dijsselbloem said a last minute request by Greek Prime Minister Alexis Tsipras to extend Greece's bailout programme had fallen on deaf ears.
"We're beyond that point, it comes too late," he told Reuters.
He said that as a member of the euro zone and European Union, Greece was welcome to request a new assistance programme, but it would come with strings attached.
"That is quite a procedure to go through," he said. "In the meantime the situation in Greece, the economy, the Greek banks, has deteriorated, unfortunately even more, so that's a difficult path to consider."
German Chancellor Angela Merkel earlier said that Germany would not negotiate on a new bailout agreement before Greece's referendum which is planned for Sunday.
She said that this applied regardless of whether new offers were made on Tuesday, suggesting it was now too late to vet them. Merkel placed the blame on the Greek government for allowing its bailout programme to expire tonight.
"Before a referendum, as planned, is carried out, we won't negotiate on anything new at all," Merkel said.
Merkel said the Greek government had been warned for weeks that the time for a bailout extension was running out and that Germany's Bundestag would have to approve such a step, which was now no longer possible.
Greece pleaded for a short-term bailout extension to avert a midnight default as frantic efforts gathered pace to salvage a deal that could keep Athens in the euro, with Germany warning that time had run out to extend vital credit lines.
As the clock ticked down towards midnight, when billions of euros in locked-up bailout funds are due to expire, euro zone finance ministers called a last-minute conference call (1700 GMT) to discuss the Greek request.
European Commission President Jean-Claude Juncker appealed to Athens to accept the deal proposed by international creditors last week while holding out hopes that some extra tweaks could still be possible.
Leftist Greek Prime Minister Alexis Tsipras, who has called a referendum for Sunday to vote on the bailout terms, responded with a counter-proposal, requesting a two-year deal covering funding support and debt restructuring, an issue the lenders have so far been reluctant to tackle.
If no agreement is reached, Greece will default on a loan to the IMF, setting it potentially on a path out of the euro with unforeseeable consequences for both the European Union's grand currency project and the global economy.
However the proposals appeared so far apart that success seemed higly unlikely.
German Chancellor Angela Merkel, whose country is Greece's biggest creditor, gave a cool response to talk of an 11th hour compromise, suggesting that there may be no time left for a deal.
"This evening at exactly midnight Central European Time the programme expires. And I am not aware of any real indications of anything else," she told a news conference.
EU and Greek government sources said Juncker, who spoke to Tsipras late on Monday, had offered to convene an emergency meeting of euro zone finance ministers to approve an aid payment to prevent Athens defaulting if the Greek leader sent a written acceptance of the terms.
However as last-ditch efforts continued, the growing risk of Athens being forced out of the single currency brought into sharp focus the chaos likely to be unleashed in Greece and the risks to the stability of the euro.
"What would happen if Greece came out of the euro? There would be a negative message that euro membership is reversible," said Spanish Prime Minister Mariano Rajoy, who a week ago declared that he did not fear contagion from Greece.
"People may think that if one country can leave the euro, others could do so in the future. I think that is the most serious problem that could arise."
The last-ditch bid from Brussels came as uncertainty built ahead of Sunday's referendum, in which Tsipras has called for a "no" vote.
Former Greek Prime Minister Antonis Samaras, leader of the main opposition party, said a "No" vote would push the country out of the single currency and wipe out wages and pensions.
The euro fell against the dollar but European shares, which dropped sharply on Monday, steadied on hopes of a deal. . The Athens stock exchange is closed during a week-long shutdown of the banking sector which began on Monday.
Opinion polls show a majority of Greeks favour holding on to the euro but a rally of tens of thousands of anti-austerity protestors in Athens on Monday highlighted the defiance many about being pushed into a corner by the lenders.
Further rallies are expected in coming days, with a demonstration in favour of staying in the euro planned in central Athens on Tuesday.
Tsipras broke off negotiations with the Commission, the IMF and the European Central Bank and announced the referendum on the bailout terms early on Saturday, giving voters just one week to debate the fundamental issues at stake.
EU leaders hammered home the message that the real choice facing Greeks is whether to stay in the euro zone or return to the drachma, even though the EU has no legal way of forcing a member state to leave the single currency.
Italian Prime Minister Matteo Renzi warned against turning the referendum into a personality contest between Tsipras and Juncker or Merkel.
"This is not a referendum on European leaders. This is a run-off vote: euro or drachma," Renzi told the Italian business daily Il Sole 24 Ore.
"The Greeks do not have to say whether they love their prime minister or the head of the European Commission more. They have to say whether they want to stay in the single currency."
Greece, which has received nearly 240 billion euros in two bailouts from the European Union and International Monetary Fund since 2010, is set to miss a 1.6 billion euro debt repayment to the IMF which falls due on Tuesday.
If that happens, IMF Managing Director Christine Lagarde will immediately report to the global lender's board at close of business, Washington time, that Greece is "in arrears" - the official euphemism for default.
Read more: Greece crisis: What happens next ?
It will be the first time in the history of the IMF that an advanced economy has defaulted on a loan from the world's financial backstop, putting Athens, which has seen its economy contract by more than 25 percent since 2009, in the same bracket as Zimbabwe, Sudan and Cuba.
Already the imposition of capital controls to prevent the crippled banking system from collapsing have given Greeks a bitter foretaste of the economic plunge that could follow exit from the euro.
Withdrawal limits of 60 euros a day have been fixed for cash machines and there have been long queues at petrol stations and in supermarkets as worried shoppers have stocked up on essentials like pasta and rice.
There were no immediate signs of serious shortages but if the banks remain closed, cash flow problems which have already been reported by some firms, could worsen.
"So far there are no problems with suppliers, but if the banks are still closed next week there will be a bit of a problem if they demand purely cash payments," said Charisis Golas, owner of a small meat and dairy shop in Athens.
The president of the European Commission, Jean-Claude Juncker, has told Greeks that saying 'No' to a bailout deal would be a vote to ditch the euro. Greece's Finance Minister Yanis Varoufakis has said Greece had no intention of quitting and cannot be forced out.
Because of its classical past as the founder of democracy, Greece was treated more tolerantly than other countries would have been when, during the 19th century, it defaulted several times on its commercial creditors.
In the end the Greeks were left with no choice. They had to use the nuclear option when it became clear that Troika technocrats are not interested in negotiating, but view them as nothing more than a Vichy government in place to rubber-stamp their policies.