Greece and its European creditors are to discuss a last-minute proposal by Athens for a new two-year rescue deal, submitted just hours before the country's international bailout expires and it loses access to European funds worth billions.
At 11pm BST, the country is also set to become the first developed nation not to pay its debts to the International Monetary Fund (IMF) on time, as Greece sinks deeper into a financial emergency that has forced it place a nationwide lockdown on money withdrawals.
The crisis worsened over the weekend after prime minister Alexis Tsipras called a referendum for this Sunday on creditors' proposals for reforms in return for bailout loans.
The move increased fears the country could soon fall out of the euro currency bloc and Greeks rushed to pull money out of ATMS.
Mr Tsipras is advocating a "no" vote.
Greece's latest offer involves a proposal to tap Europe's bailout fund - the so-called European Stability Mechanism, a pot of money set up after Greece's rescue programmes to help countries in need.
The prime minister's office said the proposal was "for the full coverage of (Greece's) financing needs with the simultaneous restructuring of the debt", but provided no further details.
Jeroen Dijsselbloem, the eurozone's top finance official, said finance ministers would have a teleconference this evening to assess the proposal.
Speculation had grown over the day that an 11th-hour deal might be possible, and markets edged up.
On Monday, European Commission president Jean-Claude Juncker made a last-minute offer. Under that proposal, Mr Tsipras would need to write to Juncker and other leaders saying he accepts the creditors' offer, which was on the table last weekend. He would also have to change his position on Sunday's referendum.
Beyond accepting the creditors' proposal, Commission spokesman Margaritis Schinas said the offer would also involve unspecified discussions on Athens's massive debt load of more than €300 billion and around 180 per cent of GDP. The Greek side has long called for debt relief, saying its current level is unsustainable.
Earlier, German chancellor Angela Merkel had dampened hopes of a quick deal to extend the existing bailout.
She said in Berlin: "The programme runs out tonight, at exactly midnight central European time. I know of no solid indications to the contrary."
However, she had said talks could continue with Athens even after the deadline.
"Of course, we are not going to cut off our channels of communication after midnight tonight.
"That means that the door is open for talks, but that is all I can say at this hour."
A Greek government official said Mr Tsipras had spoken earlier in the day with Mr Juncker, European Central Bank chief Mario Draghi and European Parliament president Martin Schulz, but no details on what was discussed were forthcoming.
Greece is expected to miss a €1.6 billion debt repayment to the IMF, due today. Finance minister Yanis Varoufakis, when asked whether Greece would make the repayment, replied: "No."
If Greece does not pay, it will be officially in arrears and will no longer have access to funding from the body until it pays its debt. This, IMF chief Christine Lagarde said last week, has "never happened in the case of an advanced economy".
EU officials also said Greece would lose access to more than €16 billion in financial support once its bailout expires.
Greece can apply for some other form of assistance but this could take days, even weeks, to organise. An assessment would first have to be made on whether Greece is eligible, what kind of terms the new package would function under, and the kinds of reforms that Athens would undertake in return.
European officials and Greek opposition parties have been adamant that a "no" vote in Sunday's referendum will mean Greece will leave the euro and possibly even the EU.
The government says this is scaremongering, and that a rejection of creditor demands will mean the country is in a better negotiating position.
On the streets of Athens, long queues formed again at ATM machines as Greeks struggled with the new capital controls imposed Monday, after a bank run over the weekend following the referendum announcement.
Cash withdrawals have been limited to €60 per day. Banks are to remain shut until at least next Monday.
The elderly have been hit particularly hard, with tens of thousands of pensions unpaid as of Tuesday afternoon. Many also found themselves completely cut off from any cash as they do not have bank cards.
The finance ministry said it would open about 1,000 bank branches across the country for three days from Wednesday to allow pensioners without bank cards to make withdrawals. But the limit would be set at €120 for the whole week, rather than the €60 per day allowed for those with bank cards.
The crisis has disturbed global markets as investors fret over the repercussions of a Greek debt default and its exit from the euro - developments that could derail a fragile global economic recovery, as well as raise questions over the long-term viability of the euro currency.