Greece has slipped deeper into its financial abyss, with the bailout programme it has relied on for five years set to expire and the country due to become the first developed nation to miss a payment to the International Monetary Fund (IMF).

After Greece made a last-ditch proposal to extend its bailout, the creditors decided in a teleconference that there was no way they could reach a deal.

Greece's international bailout expires at midnight Central European Time, after which the country loses access to billions of euro in funds. At the same time, Greece has said it will not be able to make a payment of €1.6 billion to the IMF.

An EU official said Greece's creditors would not agree tonight on a new bailout deal or extension and would instead, from tomorrow, focus on a new plan for the country.

There was "clearly no agreement tonight", said the official, adding the eurozone's finance ministers would reconvene tomorrow to discuss "a follow-up agreement".

The brinkmanship that has characterised Greece's bailout negotiations with its European creditors and the IMF rose several notches over the weekend, when Prime Minister Alexis Tsipras announced he would put a deal proposal by creditors to a referendum on Sunday. He is advocating a No vote.

The move increased fears the country could soon fall out of the euro currency bloc and Greeks rushed to pull money out of ATMs, leading the government to impose restrictions on banking transactions for at least a week.

Greeks are now limited to cash withdrawals of €60 a day and cannot send money abroad or make international payments without special permission.

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.

Hopes for an 11th-hour deal before the deadline were raised when the Greek side announced it had submitted a new deal proposal this afternoon, and the eurozone's 19 finance ministers held a teleconference to discuss it.

But those hopes were quickly dashed.

German chancellor Angela Merkel said she ruled out further negotiations with Greece before Sunday's referendum on whether to accept creditors' demands for budget reforms.

"Before the planned referendum is carried out, we will not negotiate over anything new," Ms Merkel was quoted as telling members of her party.

Earlier, she had said talks could continue after tonight's deadlines expired.

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.

Mr Tsipras' office said the proposal was "for the full coverage of (Greece's) financing needs with the simultaneous restructuring of the debt".

"Tonight we have sent a letter (to the eurogroup) that narrows the differences further," Greece's Deputy Prime Minister Yannis Dragasakis said. "We are making an additional effort. There are six points where this effort can be made. I don't want to get into specifics. But it includes pensions and labour issues."

Speaking about the latest Greek proposal, the EU official said the creditors insist that loans must come with conditions. Over the past five years of Greece's bailout, the creditors have insisted on budget cuts, tax increases and economic reforms.

In Athens, more than 10,000 Yes vote supporters gathered outside parliament despite a thunderstorm, chanting "Europe! Europe!"

Most huddled under umbrellas, including Athens resident Sofia Matthaiou. "I don't know if we'll get a deal. But we have to press them to see reason," she said, referring to the government. "The creditors need to water down their positions, too."

The protest came a day after a similar-sized government supporters advocating a No vote held a similar demonstration.

Yesterday, European Commission president Jean-Claude Juncker made a new offer to Greece. Under that proposal, Mr Tsipras would need to accept the creditors' proposal which was on the table last weekend. He would also have to change his position on Sunday's referendum.

Commission spokesman Margaritis Schinas said the offer would also involve unspecified discussions on Athens's massive debt load of more than €300 billion, or around 180 per cent of gross domestic product. The Greek side has long called for debt relief, saying its mountainous debt is unsustainable.

A Greek government official said Mr Tsipras had earlier in the day spoken to Mr Juncker, European Central Bank chief Mario Draghi and European Parliament president Martin Schulz.

Meanwhile missing the IMF payment will cut Greece off from new loans from the organisation.

And with its bailout programme expiring, Greece will lose access to more than €16 billion in financial support it had not yet tapped, officials said.

On the streets of Athens, long queues formed again at ATM machines as Greeks struggled with the new restrictions on banking transactions.

The elderly have been hit particularly hard, with tens of thousands of pensions unpaid this 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 tomorrow to allow pensioners without bank cards to make withdrawals. But the limit would be set at €120 euro for the whole week.

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